en The TErminology for the Description of DYnamics (TEDDY) project aims to provide an ontology for dynamical behaviours, observable dynamical phenomena, and control elements of bio-models and biological systems in Systems Biology and Synthetic Biology. TErminology for the Description of DYnamics (TEDDY) http://co.mbine.org/specifications/teddy http://teddyontology.svn.sourceforge.net/svnroot/teddyontology/teddy/tags/rel-2011-08-30/teddy.owl rel-2014-04-24 (inferred) dependsOn Relates temporal behaviours [http://identifiers.org/teddy/TEDDY_0000083] to functional motifs [http://identifiers.org/teddy/TEDDY_0000003] they depend on. Links a dynamic system to the way one or several temporal behaviours [http://identifiers.org/teddy/TEDDY_0000083] are modified or related upon interaction with information external to the system considered. hasFeature hasCharacteristic Used to describe properties by means of behaviour characteristic [http://identifiers.org/teddy/TEDDY_0000002]. hasSubPart true hasSuperPart true hasOnPart true adjacentTo Two temporal behaviours [http://identifiers.org/teddy/TEDDY_0000083] are adjacentTo each other if and only if they are in phase space proximity. convergeTo A temporal behaviour [http://identifiers.org/teddy/TEDDY_0000083] convergeTo another temporal behaviour [http://identifiers.org/teddy/TEDDY_0000083] if and only if it reaches the other behaviour [http://identifiers.org/teddy/TEDDY_0000083] as time goes to either positive or negative infinity. reverseOf reverseOf links two temporal behaviours [http://identifiers.org/teddy/TEDDY_0000083] whose phase diagrams can be obtained from each other by reversing the directions of all the phase paths. transforms true below Links a bifurcation [http://identifiers.org/teddy/TEDDY_0000053] to a 'temporal behaviour' [http://identifiers.org/teddy/TEDDY_0000083] which exists below the critical value of the bifurcation parameter. above Links a bifurcation [http://identifiers.org/teddy/TEDDY_0000053] to a 'temporal behaviour' [http://identifiers.org/teddy/TEDDY_0000083] which exists above the critical value of the bifurcation parameter. For continuants: C part_of C* if and only if: given any c that instantiates C at a time t, there is some c* such that c* instantiates C* at time t, and c part_of c* at t. For processes: P part_of P* if and only if: given any p that instantiates P at a time t, there is some p* such that p* instantiates P* at time t, and p part_of p* at t. (Here part_of is the instance-level part-relation.) partOf http://obofoundry.org/ro/#OBO_REL:part_of hasValue Links a 'behaviour characteristic' [http://identifiers.org/teddy/TEDDY_0000002] to the type of its value. TEDDY_0000000 TEDDY entity A Thing related to the dynamics of bio-models and biological systems. Terms belonging to TEDDY Entities are used in descriptions of dynamical behaviours, observable dynamical phenomena, and control elements in Systems Biology and Synthetic Biology. TEDDY_0000001 curve ((obsolete)) true Obsolete: equivalent to TEDDY_0000083 'Temporal Behaviour'. TEDDY_0000002 behaviour characteristic Behaviour characteristic is a property that characterizes temporal behaviors [http://identifiers.org/teddy/TEDDY_0000083]. TEDDY_0000003 functional motif http://identifiers.org/doi/10.1371/journal.pbio.0020369 A connected graph or network consisting of M vertices and a set of edges having a particular functional significance, forming a subgraph of a larger network. http://identifiers.org/doi/10.1371/journal.pbio.0020369 Sporns O, Kötter R (2004) Motifs in Brain Networks, PLoS Biology, 2(11):e369. TEDDY_0000004 monotonicity http://mathworld.wolfram.com/MonotonicFunction.html monotone monotonic A curve is `monotonic` if successive states are ordered either entirely non-decreasing or entirely non-increasing. http://mathworld.wolfram.com/MonotonicFunction.html Weisstein, Eric W. Monotonic Function. From MathWorld--A Wolfram Web Resource. TEDDY_0000005 non-monotonic http://mathworld.wolfram.com/MonotonicFunction.html A curve is non-monotonic if it has both increasing ordered successive states and decreasing orderd succesive states. http://mathworld.wolfram.com/MonotonicFunction.html Weisstein, Eric W. Monotonic Function. From MathWorld--A Wolfram Web Resource. TEDDY_0000006 oscillation http://mathworld.wolfram.com/Oscillation.html The variation of a function which exhibits slope changes, also called the saltus of a function. A series may also oscillate, causing it not to converge. http://mathworld.wolfram.com/Oscillation.html Weisstein, Eric W. Oscillation. From MathWorld--A Wolfram Web Resource. TEDDY_0000007 strict monotonicity http://eom.springer.de/M/m064830.htm strictly monotone strictly monotonic A curve is strictly monotonic if it is monotonic [http://identifiers.org/teddy/TEDDY_0000004] and has no equal temporal successive states. http://eom.springer.de/M/m064830.htm Weisstein, Eric W. Monotonic Function. From MathWorld--A Wolfram Web Resource. TEDDY_0000008 strictly increasing http://eom.springer.de/M/m064830.htm isotonic A curve is strictly increasing if it is strictly monotonic [http://identifiers.org/teddy/TEDDY_0000007] with temporal successive states increasing ordered. http://eom.springer.de/M/m064830.htm Weisstein, Eric W. Monotonic Function. From MathWorld--A Wolfram Web Resource. TEDDY_0000009 strictly decreasing http://eom.springer.de/M/m064830.htm antitonic A curve is strictly decreasing if it is strictly monotonic [http://identifiers.org/teddy/TEDDY_0000007] with temporal successive states decreasing ordered. http://eom.springer.de/M/m064830.htm Weisstein, Eric W. Monotonic Function. From MathWorld--A Wolfram Web Resource. TEDDY_0000010 single turnaround A trajectory [http://identifiers.org/teddy/TEDDY_0000083] of the system which responds negatively to displacement from equilbrium [http://identifiers.org/teddy/TEDDY_0000086]: moving away from equilibrium the trajectory turns around and moves back towards equilibrium. TEDDY_0000011 steady state ((obsolete)) true Obsolete: equivalent to TEDDY_0000086 'Fixed Point'. TEDDY_0000012 rate of change The rate of growth/decay. TEDDY_0000013 linear rate of change http://identifiers.org/isbn/1844071448 A quantity changes linearly when its change is a constant amount over a given period of time. http://identifiers.org/isbn/1844071448 D. H. Meadows (2005) The Limits to Growth: The 30-Year Update, Rff Press, revised ed. TEDDY_0000014 exponential rate of change http://identifiers.org/isbn/1844071448 A quantity changes exponentially when its change over a given period of time is proportional to what is already there. http://identifiers.org/isbn/1844071448 D. H. Meadows (2005) The Limits to Growth: The 30-Year Update, Rff Press, revised ed. TEDDY_0000015 curve shape Characteristic describing the shape of the graph of a function. TEDDY_0000016 concave shape http://identifiers.org/isbn/0691080690 A shape of a graph of a concave function, i.e. a function whose negative is convex [http://identifiers.org/teddy/TEDDY_0000021]. http://identifiers.org/isbn/0691080690 R. T. Rockafellar (1970) Convex Analysis (Princeton Mathematical Series), Princeton Univ Pr. (p.23) TEDDY_0000017 zero rate of change http://identifiers.org/isbn/1844071448 A quantity has a zero rate of change when it neither grows nor declines. http://identifiers.org/isbn/1844071448 D. H. Meadows (2005) The Limits to Growth: The 30-Year Update, Rff Press, revised ed. TEDDY_0000018 polynomial rate of change power rate of change A quantity changes polynomially when its change function is bounded above by a polinomial function. TEDDY_0000019 linear increasing A curve is linear increasing if it is is strictly increasing with a linear rate of change. TEDDY_0000020 linear decreasing A curve is linear decreasing if it is is strictly decreasing with a linear rate of change. TEDDY_0000021 convex shape http://identifiers.org/isbn/0691080690 A shape of a graph of a convex function, i.e. a function whose epigraph (the set of points on or above the graph of the function) is a convex as a subset of R^n. A subset G of a linear space is said to be convex, if it contains the whole segment (closed straight line segment) joining each of its two points. http://identifiers.org/isbn/0691080690 R. T. Rockafellar (1970) Convex Analysis (Princeton Mathematical Series), Princeton Univ Pr. (p.10, 23) TEDDY_0000022 straight line shape A shape of a graph of a linear function. TEDDY_0000023 curve characteristic A characteristic of the 'temporal behaviour' [http://identifiers.org/teddy/TEDDY_0000083] curve (projection of the function graph onto a single variable). TEDDY_0000024 unbounded growth ((obsolete)) true TEDDY_0000025 limit http://eom.springer.de/L/l058820.htm One of the fundamental concepts in mathematics, meaning that a variable depending on another variable arbitrary closely approaches some constant as the latter variable changes in a definite manner. http://eom.springer.de/L/l058820.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. TEDDY_0000026 asymptotic limit http://eom.springer.de/a/a012870.htm approximate limit A limit of a function f(x) as x->x0 over a set E for which x0 is a density point. http://eom.springer.de/a/a012870.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. TEDDY_0000027 asymptotic upper limit http://eom.springer.de/a/a012870.htm approximate upper limit An approximate upper limit of a function f(x) at a point x0 is the lower bound of the set of numbers y (including y=positive infinity) for which x0 is a point of dispersion of the set {x: f(x)>y}. http://eom.springer.de/a/a012870.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. TEDDY_0000028 asymptotic lower limit http://eom.springer.de/a/a012870.htm approximate lower limit An approximate lower limit of a function f(x) at a point x0 is the upper bound of the set of numbers y (including y=negative infinity) for which x0 is a point of dispersion of the set {x: f(x)<y}. http://eom.springer.de/a/a012870.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. TEDDY_0000029 plus infinity limit http://eom.springer.de/I/i050930.htm A function of x approaches plus infinity if its value becomes and remains larger than any given number as a result of variation of x. http://eom.springer.de/I/i050930.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. TEDDY_0000030 infinite limit http://eom.springer.de/I/i050930.htm A function of a variable x has an infinite limit if its absolute value becomes and remains larger than any given number as a result of variation of x. http://eom.springer.de/I/i050930.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. TEDDY_0000031 minus infinity limit http://eom.springer.de/I/i050930.htm A function of x approaches minus infinity if its value becomes and remains smaller than any given number as a result of variation of x. http://eom.springer.de/I/i050930.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. TEDDY_0000032 sigmoid shape http://identifiers.org/isbn/3540605053 A shape of a graph of a sigmoid function, i.e. a real function sc: R->(0,1) defined by the expression sc(x) = 1/(1 + e^(-cx)). http://identifiers.org/isbn/3540605053 R. Rojas (1996) Neural Networks: A Systematic Introduction, Springer, 1st ed. (p.149) TEDDY_0000033 feedback loop http://identifiers.org/isbn/1584886420 feedback A process whereby some proportion of function of the output signal of a system is passed (fed back) to the input. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.266) TEDDY_0000034 negative feedback loop http://identifiers.org/doi/10.1016/j.febslet.2005.02.008 negative feedback A component or variable of a system is subject to negative feedback when it inhibits its own level of activity. http://identifiers.org/doi/10.1016/j.febslet.2005.02.008 Wolkenhauer O, Ullah M, Wellstead P, Cho K-H (2005) The dynamic systems approach to control and regulation of intracellular networks, FEBS Letters, 579 (8): 1846-1853. TEDDY_0000035 positive feedback loop http://identifiers.org/doi/10.1016/j.febslet.2005.02.008 positive feedback A component or variable of a system is subject to positive feedback when it increases its own level of activity. http://identifiers.org/doi/10.1016/j.febslet.2005.02.008 Wolkenhauer O, Ullah M, Wellstead P, Cho K-H (2005) The dynamic systems approach to control and regulation of intracellular networks, FEBS Letters, 579 (8): 1846-1853. TEDDY_0000036 feed-forward loop FFL feed-forward feedforward feedforward loop A 'three-node feed-forward loop' [http://identifiers.org/teddy/TEDDY_0000037] or its topological generalization. TEDDY_0000037 three-node feed-forward loop http://identifiers.org/isbn/1584886420 3-node FFL 3-node feed-forward 3-node feed-forward loop 3-node feedforward 3-node feedforward loop FFL thre-node FFL three-node feedforward loop A pattern with three nodes, X, Y, and Z, in which X has a directed edge to Y and Z, and Y has a directed edge to Z. The FFL is a network motif in many biological networks, and can perform a variety of tasks (such as sign-sensitive delay, sign-sensitive acceleration, and pulse generation). http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.267) FFL http://identifiers.org/isbn/1584886420 (p.41) TEDDY_0000038 coherent three-node feed-forward loop http://identifiers.org/isbn/1584886420 coherent 3-node feed-forward loop coherent 3-node feedforward coherent 3-node feedforward loop coherent three-node feedforward loop A feed-forward loop [http://identifiers.org/teddy/TEDDY_0000037] in which the sign of the direct path from X to Z is the same as the overall sign of the indirect path from X through Y to Z. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.265) TEDDY_0000039 type-1 coherent three-node feed-forward loop http://identifiers.org/isbn/1584886420 C1-FFL coherent 3-node feedforward type-1 type-1 coherent FFL A 'coherent three-node feed-forward loop' [http://identifiers.org/teddy/TEDDY_0000038] in which all three regulations are positive. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47) TEDDY_0000040 type-2 coherent three-node feed-forward loop http://identifiers.org/isbn/1584886420 C2-FFL coherent 3-node feedforward type-2 type-2 coherent FFL A 'coherent three-node feed-forward loop' [http://identifiers.org/teddy/TEDDY_0000038] in which X represses Z, and also represses an activator of Z. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47) TEDDY_0000041 type-3 coherent three-node feed-forward loop http://identifiers.org/isbn/1584886420 C3-FFL coherent 3-node feedforward type-3 type-3 coherent FFL A 'coherent three-node feed-forward loop' [http://identifiers.org/teddy/TEDDY_0000038] in which X represses Z, and also activates a repressor of Z. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47) TEDDY_0000042 type-4 coherent three-node feed-forward loop http://identifiers.org/isbn/1584886420 C4-FFL coherent 3-node feedforward type-4 type-4 coherent FFL A 'coherent three-node feed-forward loop' [http://identifiers.org/teddy/TEDDY_0000038] in which X activates Z, and also represses a repressor of Z. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47) TEDDY_0000043 incoherent three-node feed-forward loop http://identifiers.org/isbn/1584886420 incoherent 3-node feed-forward loop incoherent 3-node feedforward incoherent 3-node feedforward loop incoherent three-node feedforward loop A feed-forward loop [http://identifiers.org/teddy/TEDDY_0000037] in which the sign of the direct path from X to Z is the opposite as the overall sign of the indirect path from X through Y to Z. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.267) TEDDY_0000044 type-1 incoherent three-node feed-forward loop http://identifiers.org/isbn/1584886420 I1-FFL incoherent 3-node feedforward type-1 type-1 incoherent FFL An 'incoherent three-node feed-forward loop' [http://identifiers.org/teddy/TEDDY_0000043] in which X activates Z, and also activates a repressor of Z. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47) TEDDY_0000045 type-2 incoherent three-node feed-forward loop http://identifiers.org/isbn/1584886420 I2-FFL incoherent 3-node feedforward type-2 type-2 incoherent FFL An 'incoherent three-node feed-forward loop' [http://identifiers.org/teddy/TEDDY_0000043] in which X represses Z, and also represses a repressor of Z. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47) TEDDY_0000046 type-3 incoherent three-node feed-forward loop http://identifiers.org/isbn/1584886420 I3-FFL incoherent 3-node feedforward type-3 type-3 incoherent FFL An 'incoherent three-node feed-forward loop' [http://identifiers.org/teddy/TEDDY_0000043] in which X represses Z, and also activates an activator of Z. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47) TEDDY_0000047 type-4 incoherent three-node feed-forward loop http://identifiers.org/isbn/1584886420 I4-FFL incoherent 3-node feedforward type-4 type-4 incoherent FFL An 'incoherent three-node feed-forward loop' [http://identifiers.org/teddy/TEDDY_0000043] in which X activates Z, and also represses an activator of Z. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47) TEDDY_0000048 orbit ((obsolete)) true Obsolete: equivalent to TEDDY_0000083 'Temporal Behaviour'. TEDDY_0000049 fixed point ((obsolete)) true Obsolete: equivalent to TEDDY_0000086 'Fixed Point'. TEDDY_0000050 periodic orbit http://identifiers.org/isbn/0387983821 closed orbit cycle periodic solution A temporal behaviour [http://identifiers.org/teddy/TEDDY_0000083] which repeats every state after a specific period of time. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.9) TEDDY_0000051 limit cycle http://identifiers.org/isbn/0738204536 Grenzzyklus isolated closed path A closed orbit which is isolated, i.e. neighbouring orbits are not closed. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.196) Grenzzyklus http://identifiers.org/isbn/3817112823 isolated closed path http://identifiers.org/isbn/0198565623 (p.30) TEDDY_0000052 parameter dependency ((obsolete)) true Obsolete: not required anymore. TEDDY_0000053 bifurcation http://identifiers.org/isbn/0198565623 http://www.egwald.com/nonlineardynamics/bifurcations.php A `characteristic` describing a sudden qualitative (topological) change in the orbit structure of a system occuring as a parameter passes through a critical value, called a bifurcation point. http://identifiers.org/isbn/0198565623 Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.420) http://www.egwald.com/nonlineardynamics/bifurcations.php Elmer G. Wiens: Egwald Web Services Ltd. TEDDY_0000054 strange attractor http://identifiers.org/isbn/0738204536 http://identifiers.org/isbn/9810221428 chaotic attractor fractal attractor A non-periodic orbit [http://identifiers.org/teddy/TEDDY_0000143] which is attracting and exhibits sensitive dependence on initial conditions. The attractor [http://identifiers.org/teddy/TEDDY_0000094] is strange if trajectories [http://identifiers.org/teddy/TEDDY_0000083] on the attractor, being stable according to Poisson [http://identifiers.org/teddy/TEDDY_0000149], are unstable according to Lyapunov [not TEDDY_0000113]. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.325) http://identifiers.org/isbn/9810221428 V. S. Anishchenko (1995) Dynamical Chaos-Models and Experiments: Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific Series on Nonlinear Science, Series a, Vol 8). World Scientific Pub Co Inc. (p.10) chaotic attractor http://identifiers.org/isbn/0738204536 (p.325) fractal attractor http://identifiers.org/isbn/0738204536 (p.325) TEDDY_0000055 bursting http://identifiers.org/isbn/0262090430 A burst is two or more spikes followed by a period of quiescence. http://identifiers.org/isbn/0262090430 Izhikevich EM (2007) Dynamical systems in neuroscience : the geometry of excitability and bursting, MIT Press. (p.325) TEDDY_0000056 switch http://identifiers.org/doi/10.1371/journal.pcbi.1002085 A signaling network that converts a graded input cue into a binary, all-or-none response is said to exhibit ‘switch-like’ behavior; switching enables the establishment of discrete states which is vital in processes such as cell proliferation and differentiation. http://identifiers.org/doi/10.1371/journal.pcbi.1002085 Shah NA, Sarkar CA (2011) Robust Network Topologies for Generating Switch-Like Cellular Responses, PLoS Comput Biol.; 7(6): e1002085. TEDDY_0000057 stability ((obsolete)) true Obsolete: not required anymore. TEDDY_0000058 use 'strictly decreasing' [http://identifiers.org/teddy/TEDDY_0000009] and 'asymptotic limit' [http://identifiers.org/teddy/TEDDY_0000026] terms instead. asymptotic decreasing ((obsolete)) http://eom.springer.de/A/a013610.htm true Asymptote of a curve y=f(x) with an infinite branch is a straight line the distance of which from the point (x, f(x)) on the curve tends to zero as the point moves along the branch of the curve to infinity. Decreasing function having for which an asymptote exists is called 'asymptotic decreasing'. http://eom.springer.de/A/a013610.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. TEDDY_0000059 use 'strictly increasing' [http://identifiers.org/teddy/TEDDY_0000008] and 'asymptotic limit' [http://identifiers.org/teddy/TEDDY_0000026] terms instead. asymptotic increasing ((obsolete)) http://eom.springer.de/A/a013610.htm true Asymptote of a curve y=f(x) with an infinite branch is a straight line the distance of which from the point (x, f(x)) on the curve tends to zero as the point moves along the branch of the curve to infinity. Increasing function having for which an asymptote exists is called 'asymptotic increasing'. http://eom.springer.de/A/a013610.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. TEDDY_0000060 use 'strictly increasing' [http://identifiers.org/teddy/TEDDY_0000008] and 'infinite limit' [http://identifiers.org/teddy/TEDDY_0000030] terms instead. diverging increasing ((obsolete)) true TEDDY_0000061 chaotic oscillation http://identifiers.org/isbn/9810221428 non-periodic oscillation If a particular solution is aperiodic, but bounded for pt->infinity, then it corresponds to the regime of chaotic oscillation. http://identifiers.org/isbn/9810221428 V. S. Anishchenko (1995) Dynamical Chaos-Models and Experiments: Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific Series on Nonlinear Science, Series a, Vol 8). World Scientific Pub Co Inc. (p.10) TEDDY_0000062 sustained oscillation ((obsolete)) true Obsolete: equivalent to TEDDY_0000051 'Limit Cycle'. TEDDY_0000063 damped oscillation http://identifiers.org/isbn/0486655083 Damping is any effect that tends to reduce the amplitude [http://identifiers.org/teddy/TEDDY_0000131] of oscillations in an oscillatory system. http://identifiers.org/isbn/0486655083 A. A. Andronov, A. A. Vitt, and S. E. Khaikin (1987) Theory of Oscillators, Dover Publications. TEDDY_0000064 single-periodic oscillation http://identifiers.org/isbn/0198565623 SPO single periodic oscillation An oscillation [http://identifiers.org/teddy/TEDDY_0000006] corresponding to a solution having a one-loop phase path and a period-1 Poincaré map. http://identifiers.org/isbn/0198565623 Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.465) TEDDY_0000065 mixed-mode oscillation http://identifiers.org/doi/10.1063/1.2900015 MMO Mixed-mode oscillations are complex periodic waveforms where each period is comprised of several maxima and minima of different amplitudes [http://identifiers.org/teddy/TEDDY_0000131]. mixed-mode oscillation I. Erchova and D. J. McGonigle (2008) Rhythms of the brain: an examination of mixed mode oscillation approaches to the analysis of neurophysiological data, Chaos (Woodbury, N.Y.) 18. http://identifiers.org/doi/10.1063/1.2900015 I. Erchova & D. J. McGonigle (2008) Rhythms of the brain: an examination of mixed mode oscillation approaches to the analysis of neurophysiological data. Chaos (Woodbury, N.Y.) 18(1). TEDDY_0000066 periodic oscillation http://identifiers.org/isbn/9810221428 The characteristic of a periodic solution (a solution which is distinguished by the condition x*(t) = x*(t+T), where T is the period [http://identifiers.org/teddy/TEDDY_0000067] of solution). http://identifiers.org/isbn/9810221428 V. S. Anishchenko (1995) Dynamical Chaos-Models and Experiments: Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific Series on Nonlinear Science, Series a, Vol 8). World Scientific Pub Co Inc. (p.6) TEDDY_0000067 period http://eom.springer.de/p/p072210.htm For a periodic solution x(t), there is a number T, not equal to 0, such that x(t+T) = x(t) for t ∈ R. All possible such T are called periods of this periodic solution; the continuity of x(t) implies that either x(t) is independent of t or that all possible periods are integral multiples of one of them — the minimal period T0>0. When one speaks of a periodic solution, it is often understood that the second case applies, and T0 is simply termed the period. http://eom.springer.de/p/p072210.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. TEDDY_0000068 regularity ((obsolete)) true Obsolete: not required anymore. TEDDY_0000069 local bifurcation http://en.wikipedia.org/wiki/Bifurcation_theory#Local_bifurcations http://identifiers.org/isbn/0387983821 bifurcation from steady state bifurcation of equilibrium bifurcation of equilibrium point bifurcation of fixed point A `bifurcation` [http://identifiers.org/teddy/TEDDY_0000053] in which a stable [http://identifiers.org/teddy/TEDDY_0000133] fixed point [http://identifiers.org/teddy/TEDDY_0000086] changes to an unstable [not TEDDY_0000133] one or vanishes. It can be detected within any small neighborhood of the fixed point: the real part of the eigenvalue of the linarisation around the fixed point is zero at the bifurcation. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.58) bifurcation from steady state http://www.scholarpedia.org/article/MATCONT bifurcation of equilibrium http://identifiers.org/isbn/0387983821 (p.58) bifurcation of fixed point http://identifiers.org/isbn/0387983821 (p.58) TEDDY_0000070 bifurcation of limit cycle http://identifiers.org/isbn/0387983821 A global bifurcation [http://identifiers.org/teddy/TEDDY_0000147] in which a limit cycle [http://identifiers.org/teddy/TEDDY_0000051] (dis)appears or changes its stability [http://identifiers.org/teddy/TEDDY_0000113]. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.162ff) 1 1 1 1 TEDDY_0000071 saddle-node bifurcation http://identifiers.org/isbn/0387983821 http://identifiers.org/isbn/0738204536 blue sky bifurcation fold bifurcation limit point bifurcation tangent bifurcation turning-point bifurcation A `zero-eigenvalue bifurcation` [http://identifiers.org/teddy/TEDDY_0000123] in which a stable [http://identifiers.org/teddy/TEDDY_0000133] fixed point [http://identifiers.org/teddy/TEDDY_0000086] and an unstable [not TEDDY_0000133] fixed point [http://identifiers.org/teddy/TEDDY_0000086] collide and mutually annihilate. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.80) http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.45) blue sky bifurcation http://identifiers.org/isbn/0738204536 (p.47) fold bifurcation http://identifiers.org/isbn/0738204536 (p.47) limit point bifurcation http://www.scholarpedia.org/article/Saddle-node_Bifurcation tangent bifurcation http://identifiers.org/isbn/0387983821 (p.80) turning-point bifurcation http://identifiers.org/isbn/0738204536 (p.47) TEDDY_0000072 Hopf bifurcation http://identifiers.org/isbn/0738204536 Andronov-Hopf Bifurcation A `local bifurcation` [http://identifiers.org/teddy/TEDDY_0000069] in which a `stable spiral` [http://identifiers.org/teddy/TEDDY_0000126] changes in an `unstable spiral` [http://identifiers.org/teddy/TEDDY_0000127]. The linearisation around the fixed point [http://identifiers.org/teddy/TEDDY_0000086] has two conjugate eigenvalues. This eigenvalues cross simultaneously the imaginary axis from left (negative real part) to the right during the bifurcation. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.248ff) Andronov-Hopf Bifurcation http://identifiers.org/isbn/0387983821 (p.80) TEDDY_0000073 subcritical Hopf bifurcation http://identifiers.org/isbn/0387983821 subc-AH subcritical Andronov-Hopf bifurcation A `Hopf bifurcation` [http://identifiers.org/teddy/TEDDY_0000072] in which an `unstable limit cycle` [http://identifiers.org/teddy/TEDDY_0000128] is destroyed. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.88) subc-AH http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors subcritical Andronov-Hopf bifurcation http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors TEDDY_0000074 supercritical Hopf bifurcation http://identifiers.org/isbn/0738204536 supc-AH supercritical Andronov-Hopf bifurcation A `Hopf bifurcation` [http://identifiers.org/teddy/TEDDY_0000072] in which an `stable limit cycle` [http://identifiers.org/teddy/TEDDY_0000114] appears. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.249) supc-AH http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors supercritical Andronov-Hopf bifurcation http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors TEDDY_0000075 saddle-node on invariant circle bifurcation http://identifiers.org/isbn/0262090430 SNIC SNIC bifurcation SNLC SNLC bifurcation saddle-node on limit cycle bifurcation Saddle-node bifurcation on invariant circle occurs when the center manifold of a saddle-node bifurcation [http://identifiers.org/teddy/TEDDY_0000071] forms an invariant circle. Such a bifurcation results in (dis)appearance of a limit cycle [http://identifiers.org/teddy/TEDDY_0000051] of an infinite period. http://identifiers.org/isbn/0262090430 Izhikevich EM (2007) Dynamical systems in neuroscience : the geometry of excitability and bursting, MIT Press. SNIC http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors SNIC bifurcation http://www.scholarpedia.org/article/Saddle-node_bifurcation_on_invariant_circle SNLC http://www.scholarpedia.org/article/Saddle-node_bifurcation_on_invariant_circle SNLC bifurcation http://www.scholarpedia.org/article/Saddle-node_bifurcation_on_invariant_circle saddle-node on limit cycle bifurcation http://www.scholarpedia.org/article/Saddle-node_bifurcation_on_invariant_circle 2 0 TEDDY_0000076 saddle-node bifurcation of limit cycles http://identifiers.org/isbn/0387983821 fold bifurcation of limit cycles A 'bifurcation of limit cycle' [http://identifiers.org/teddy/TEDDY_0000070] in which two limit cycles [http://identifiers.org/teddy/TEDDY_0000051] (stable [http://identifiers.org/teddy/TEDDY_0000114] and saddle) collide and disappear. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.163) fold bifurcation of limit cycles http://identifiers.org/isbn/0387983821 (p. 163) TEDDY_0000077 period-doubling bifurcation of limit cycle http://identifiers.org/isbn/0387983821 flip bifurcation of limit cycle A 'bifurcation of limit cycle' [http://identifiers.org/teddy/TEDDY_0000070] in which a 'periodic orbit' [http://identifiers.org/teddy/TEDDY_0000050] with period-2 Poincaré map appears, while the fixed point changes its stability. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.163) flip bifurcation of limit cycle http://identifiers.org/isbn/0387983821 (p.163) TEDDY_0000078 Neimark-Sacker bifurcation of limit cycle http://identifiers.org/isbn/0387983821 A 'bifurcation of limit cycle' [http://identifiers.org/teddy/TEDDY_0000070] corresponding to the case when the multipliers are complex and simple and lie on the unit circle. The Poincaré map then has a parameter-dependent, two-dimensional, invariant manifold on which a closed invariant curve generically bifurcates from the fixed point. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.164) TEDDY_0000079 integrator TEDDY_0000080 _obsolete behaviour ((obsolete)) true Obsolete: only one obsolete branch required. TEDDY_0000081 _obsolete characteristic ((obsolete)) true Obsolete: only one obsolete branch required. TEDDY_0000082 _obsolete functionality ((obsolete)) true Obsolete: only one obsolete branch required. TEDDY_0000083 temporal behaviour http://identifiers.org/isbn/0387983821 orbit phase curve phase path solution curve trajectory A temporal sequence of states following the evolution operator of the dynamical system through a given initial state. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.8) orbit http://identifiers.org/isbn/0387983821 (p.8) phase path http://identifiers.org/isbn/0198565623 (p.6) solution curve http://identifiers.org/isbn/0387908196 (p.2) trajectory http://identifiers.org/isbn/0387983821 (p.8) TEDDY_0000084 parametrical behaviour ((obsolete)) true Obsolete: not required anymore. TEDDY_0000085 limit behaviour http://identifiers.org/isbn/0387983821 asymptotic state limit set A `temporal behaviour` [http://identifiers.org/teddy/TEDDY_0000083] with all behaviours starting sufficiently near converge to it as time goes to either positive or negative infinity. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.10) TEDDY_0000086 fixed point http://mathworld.wolfram.com/FixedPoint.html constant behaviour constant solution critical point equilibrium equilibrium point equilibrium solution rest solution steady state A 'temporal behaviour' [http://identifiers.org/teddy/TEDDY_0000083] which does not change its state. http://mathworld.wolfram.com/FixedPoint.html Weisstein, Eric W. Fixed Point. From MathWorld--A Wolfram Web Resource. critical point http://identifiers.org/isbn/0198565623 (p.4) equilibrium point http://identifiers.org/isbn/0198565623 (p.4) TEDDY_0000087 node http://identifiers.org/isbn/0738204536 fixed point node A 'fixed point' [http://identifiers.org/teddy/TEDDY_0000086] for which the Jacobian matrix has real-valued eigenvalues of the same sign. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137) TEDDY_0000088 center http://identifiers.org/isbn/0738204536 centre elliptic fixed point A 'fixed point' [http://identifiers.org/teddy/TEDDY_0000086] for which the Jacobian matrix has purely imaginary complex conjugate eigenvalues. The fixed point is surrounded by a family of cycles in the phase portrait. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (pp.134,137) TEDDY_0000089 saddle http://identifiers.org/isbn/0738204536 saddle point A 'fixed point' [http://identifiers.org/teddy/TEDDY_0000086] for which the Jacobian matrix has real-valued eigenvalues of opposite signs. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137) saddle point http://identifiers.org/isbn/0198565623 (p.73) TEDDY_0000090 star http://identifiers.org/isbn/0738204536 proper node star point A 'fixed point' [http://identifiers.org/teddy/TEDDY_0000086] for which the Jacobian matrix has identical eigenvalues and two independent corresponding eigenvectors. All other trajectories [http://identifiers.org/teddy/TEDDY_0000083] of the system lie on straight through the fixed point. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.135) TEDDY_0000091 spiral http://identifiers.org/isbn/0738204536 focus spiral point A 'fixed point' [http://identifiers.org/teddy/TEDDY_0000086] for which the Jacobian matrix has not purely imaginary complex conjugate eigenvalues. The fixed point is surrounded by spiralling behaviours [http://identifiers.org/teddy/TEDDY_0000083]. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (pp.134,137) focus http://identifiers.org/isbn/0198565623 (p.25) spiral point http://identifiers.org/isbn/0198565623 (p.73) TEDDY_0000092 non-isolated fixed point http://identifiers.org/isbn/0738204536 A 'fixed point' [http://identifiers.org/teddy/TEDDY_0000086] for which at least one eigenvalue of the Jacobian matrix is zero. If the other eigenvalue is non-zero the system has an entire line of fixed points along one dimension. If both eigenvalues are zero the system has a entire plane of fixed points. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (pp.128,137) TEDDY_0000093 degenerate node http://identifiers.org/isbn/0738204536 degenerated node improper node A 'fixed point' [http://identifiers.org/teddy/TEDDY_0000086] for which the Jacobian matrix has identical eigenvalues and only one independent eigenvector. All other trajectories [http://identifiers.org/teddy/TEDDY_0000083] of the system asymptotically become parallel to the unique eigendirection. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.135f) TEDDY_0000094 attractor http://identifiers.org/isbn/0738204536 http://identifiers.org/isbn/9810221428 The limit set which corresponds to the particular type of stable solution and attracts phase trajectories [http://identifiers.org/teddy/TEDDY_0000083] from a sertan region of initial conditions is an attractor. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.324) http://identifiers.org/isbn/9810221428 V. S. Anishchenko (1995) Dynamical Chaos-Models and Experiments: Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific Series on Nonlinear Science, Series a, Vol 8). World Scientific Pub Co Inc. (p.10) TEDDY_0000095 Lyapunov stable fixed point http://identifiers.org/isbn/0738204536 Liapunov stable fixed point A 'fixed point' [http://identifiers.org/teddy/TEDDY_0000086] which is Liapunov stable [http://identifiers.org/teddy/TEDDY_0000133]. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129) TEDDY_0000096 unstable ((obsolete)) http://identifiers.org/isbn/0738204536 true Obsolete: a limit behaviour is unstable if it is neither Liapunov stable nor stable (use repellor instead). http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129) TEDDY_0000097 asymptotic stability http://identifiers.org/isbn/0738204536 stable behaviour A `stable behaviour` which is also a `Liapunov stable behaviour`. The solution x*(t), t >= t0 is asymptotically stable, if all sufficiently small disturbances of the initial value lead to the solutions which re-approach the undisturbed solution. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129) stable behaviour http://identifiers.org/isbn/0738204536, (p.129) TEDDY_0000098 neutral stability http://identifiers.org/isbn/0738204536 asymptotically unstable A behaviour [http://identifiers.org/teddy/TEDDY_0000083] which is Liapunov stable [http://identifiers.org/teddy/TEDDY_0000133] and not attracting [http://identifiers.org/teddy/TEDDY_0000097]. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129) asymptotically unstable http://identifiers.org/isbn/0198565623 (p.289) 1 2 TEDDY_0000099 saddle connection http://identifiers.org/isbn/0738204536 A temporal behaviour [http://identifiers.org/teddy/TEDDY_0000083] connecting two saddle points [http://identifiers.org/teddy/TEDDY_0000089]. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.184) 1 TEDDY_0000100 homoclinic saddle connection http://identifiers.org/isbn/0738204536 homoclinic saddle loop saddle loop A saddle connection [http://identifiers.org/teddy/TEDDY_0000099] connecting a saddle point [http://identifiers.org/teddy/TEDDY_0000089] to itself. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.161) homoclinic saddle loop http://identifiers.org/isbn/3540971416 (p.213) saddle loop http://www.egwald.ca/nonlineardynamics/mathappendix.php#limitset 2 TEDDY_0000101 heteroclinic saddle connection http://identifiers.org/isbn/0738204536 heteroclinic saddle trajectory saddle connection A saddle connection [http://identifiers.org/teddy/TEDDY_0000099] connecting two different saddle points [http://identifiers.org/teddy/TEDDY_0000089]. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.166) heteroclinic saddle trajectory http://identifiers.org/isbn/0738204536 (p.166) saddle connection The term `saddle connection` is used as a synonym for a heteroclinic orbit (http://identifiers.org/isbn/0738204536 (p.166) ). But `saddle connection` is also used for both: homoclinic and heteroclinic orbits (http://identifiers.org/isbn/0387943773 (p.184)). http://identifiers.org/isbn/0738204536 (p.166) TEDDY_0000102 repeller http://eom.springer.de/R/r081310.htm repelling set repellor A subset of the phase space of the system that is an attractor [http://identifiers.org/teddy/TEDDY_0000094] for the reverse [TR_0015] system. http://eom.springer.de/R/r081310.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. repelling set http://eom.springer.de/R/r081310.htm TEDDY_0000103 rdfs:label follows notation in http://identifiers.org/isbn/3817112823 (p.42). stable ((obsolete)) http://identifiers.org/isbn/0738204536 true attracting Obsolete: a limit behaviour [http://identifiers.org/teddy/TEDDY_0000085] is stable if all behaviours starting sufficiently near to it will approach it as time goes to positive infinity (use attractor instead). http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.128) TEDDY_0000104 half-stable fixed point http://identifiers.org/isbn/0738204536 A 'fixed point' [http://identifiers.org/teddy/TEDDY_0000086] which is half-stable [http://identifiers.org/teddy/TEDDY_0000134], i.e. the fixed point is attracting in one direction and unstable in the other direction. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.26) TEDDY_0000105 neutrally stable behaviour ((obsolete)) http://identifiers.org/isbn/0738204536 true Non-Isolated Asymptotic Behaviour Obsolete: a temporal behaviour which is neither attracting nor unstable (equivalent to 'neutrally stable' [http://identifiers.org/teddy/TEDDY_0000098]). http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129) TEDDY_0000106 non-isolated cycle http://identifiers.org/isbn/0738204536 neutrally stable cycle A cycle which is surrounded by other cycles. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.196) TEDDY_0000107 temporal behaviour ((obsolete)) true Obsolete: equivalent to TEDDY_0000083 'Temporal Behaviour'. TEDDY_0000108 perturbation response A response to perturbations of the system or its environment. TEDDY_0000109 monostable perturbation response http://identifiers.org/doi/10.1371/journal.pone.0021782 A `perturbation response` [http://identifiers.org/teddy/TEDDY_0000108] shown by a system with a single attractor [http://identifiers.org/teddy/TEDDY_0000094]. For all initial states sufficiently near to the attractor the system tend to this attractor. http://identifiers.org/doi/10.1371/journal.pone.0021782 T. Malashchenko, et al. (2011). `Six types of multistability in a neuronal model based on slow calcium current.'. PloS one 6(7):e21782+. TEDDY_0000110 bistable perturbation response http://identifiers.org/doi/10.1371/journal.pone.0021782 A `perturbation response` [http://identifiers.org/teddy/TEDDY_0000108] shown by a system with two different attractors [http://identifiers.org/teddy/TEDDY_0000094]. Depending on the initial state the system tend to the one or the other attractor. http://identifiers.org/doi/10.1371/journal.pone.0021782 T. Malashchenko, et al. (2011). `Six types of multistability in a neuronal model based on slow calcium current.'. PloS one 6(7):e21782+. TEDDY_0000111 multistable perturbation response http://identifiers.org/doi/10.1371/journal.pone.0021782 A `perturbation response` [http://identifiers.org/teddy/TEDDY_0000108] shown by a system with more than two different attractors [http://identifiers.org/teddy/TEDDY_0000094]. Depending on the initial state the system tend to one of the attractors. http://identifiers.org/doi/10.1371/journal.pone.0021782 T. Malashchenko, et al. (2011). `Six types of multistability in a neuronal model based on slow calcium current.'. PloS one 6(7):e21782+. TEDDY_0000112 quasi-periodic oscillation http://eom.springer.de/Q/q076630.htm http://identifiers.org/isbn/0738204536 http://www.scholarpedia.org/article/Quasiperiodic_oscillations QPO quasiperiodic oscillation Quasi-periodic oscillation is an oscillation [http://identifiers.org/teddy/TEDDY_0000006] that can be described by a quasiperiodic function, i.e. a function f such that f(t)=F(t,...,t) for some continuous function F(t1,...,tn) of n variables that is periodic with respect to t1,...,tn with periods w1,...,wn, respectively. All the w1,...,wn are required to be strictly positive and their reciprocals p1,...,pn have to be rationally linearly independent. http://eom.springer.de/Q/q076630.htm Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.276) http://www.scholarpedia.org/article/Quasiperiodic_oscillations Anatoly M. Samoilenko (2007) Quasiperiodic oscillations. Scholarpedia, 2(5):1783. TEDDY_0000113 stable fixed point ((obsolete)) http://identifiers.org/isbn/0738204536 true Attractor Sink Obsolete: a fixed point which is stable. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.17) TEDDY_0000114 stable limit cycle http://identifiers.org/isbn/0738204536 If all the neighbouring paths [http://identifiers.org/teddy/TEDDY_0000083] approach the limit cycle [http://identifiers.org/teddy/TEDDY_0000051] then it is stable. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.196) TEDDY_0000115 neutrally stable fixed point http://identifiers.org/isbn/0738204536 A 'fixed point' [http://identifiers.org/teddy/TEDDY_0000086] which is neutrally stable [http://identifiers.org/teddy/TEDDY_0000098]. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129) TEDDY_0000116 magnitude A size of an object. TEDDY_0000117 high magnitude A magnitude that is much higher than the expected one. TEDDY_0000118 low magnitude A magnitude that is much lower than the expected one. TEDDY_0000119 saddle-node homoclinic bifurcation http://identifiers.org/isbn/0387983821 infinite period bifurcation A global bifurcation [http://identifiers.org/teddy/TEDDY_0000147] in which node [http://identifiers.org/teddy/TEDDY_0000087] and a saddle [http://identifiers.org/teddy/TEDDY_0000089] collide to a saddle [http://identifiers.org/teddy/TEDDY_0000089] at the bifurcation point, connected by a homoclinic saddle connection [http://identifiers.org/teddy/TEDDY_0000100]. Above the bifurcation point a limit cycle [http://identifiers.org/teddy/TEDDY_0000051] appears and the saddle [http://identifiers.org/teddy/TEDDY_0000089] vanishes. The period of this cycle tends to infinity as the parameter approaches its bifurcation value. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.59ff) infinite period bifurcation http://identifiers.org/isbn/0738204536 (p.262) TEDDY_0000120 degenerate Hopf bifurcation http://identifiers.org/isbn/0738204536 A `Hopf bifurcation` [http://identifiers.org/teddy/TEDDY_0000072] in which neigther a limit cycle [http://identifiers.org/teddy/TEDDY_0000051] is destroyed nor a limit cycle [http://identifiers.org/teddy/TEDDY_0000051] appears. On the bifurcation the fixed point [http://identifiers.org/teddy/TEDDY_0000086] is a `center` [http://identifiers.org/teddy/TEDDY_0000088]. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.253) 1 1 1 1 TEDDY_0000121 transcritical bifurcation http://identifiers.org/isbn/0738204536 A `zero-eigenvalue bifurcation` [http://identifiers.org/teddy/TEDDY_0000123] in which a stable [http://identifiers.org/teddy/TEDDY_0000133] fixed point [http://identifiers.org/teddy/TEDDY_0000086] and an unstable [not TEDDY_0000133] fixed point [http://identifiers.org/teddy/TEDDY_0000086] coalesce and exchange their stability. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.50f) 2 2 TEDDY_0000122 pitchfork bifurcation http://identifiers.org/isbn/0738204536 flip bifurcation A `zero-eigenvalue bifurcation` [http://identifiers.org/teddy/TEDDY_0000123] in which the fixed point [http://identifiers.org/teddy/TEDDY_0000086] is surrounded by two symmetrical fixed points on one side of the bifurcation. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.55) flip bifurcation http://identifiers.org/isbn/0198565623 (p.432) TEDDY_0000123 zero-eigenvalue bifurcation http://identifiers.org/isbn/0738204536 A `local bifurcation` [http://identifiers.org/teddy/TEDDY_0000069] in which one of the eigenvalue of the linarisation around the fixed point [http://identifiers.org/teddy/TEDDY_0000086] is zero at the bifurcation. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.248) 1 1 2 TEDDY_0000124 subcritical pitchfork bifurcation http://identifiers.org/isbn/0738204536 A `pitchfork bifurcation` [http://identifiers.org/teddy/TEDDY_0000122] in which two symmetrical stable [http://identifiers.org/teddy/TEDDY_0000133] fixed points [http://identifiers.org/teddy/TEDDY_0000086] collide with an unstable [not TEDDY_0000133] fixed point [http://identifiers.org/teddy/TEDDY_0000086] and dissapear, while the unstable fixed point transforms into a stable one. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.58f) 1 2 1 TEDDY_0000125 supercritical pitchfork bifurcation http://identifiers.org/isbn/0738204536 A `pitchfork bifurcation` [http://identifiers.org/teddy/TEDDY_0000122] in which two symmetrical stable [http://identifiers.org/teddy/TEDDY_0000133] fixed points [http://identifiers.org/teddy/TEDDY_0000086] and an unstable [not TEDDY_0000133] fixed point [http://identifiers.org/teddy/TEDDY_0000086] appear from a stable fixed point. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.55f) TEDDY_0000126 stable spiral http://identifiers.org/isbn/0738204536 spiral sink stable focus stable spiral point A spiral point [http://identifiers.org/teddy/TEDDY_0000091] which is stable [http://identifiers.org/teddy/TEDDY_0000133], i.e. for which the Jacobian matrix has two negative complex conjugate eigenvalues. The fixed point is surrounded by behaviours [http://identifiers.org/teddy/TEDDY_0000083] spiralling downward the fixed point, corresponding to decaying oscillations. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (pp.134,137) stable focus http://identifiers.org/isbn/0198565623 (p.25) stable spiral point http://identifiers.org/isbn/0198565623 (p.73) TEDDY_0000127 unstable spiral http://identifiers.org/isbn/0738204536 spiral source unstable focus unstable spiral point A spiral point [http://identifiers.org/teddy/TEDDY_0000091] which is unstable [not TEDDY_0000133], i.e. for which the Jacobian matrix has two positive complex conjugate eigenvalues. The fixed point is surrounded by behaviours [http://identifiers.org/teddy/TEDDY_0000083] spiralling upward the fixed point, corresponding to growing oscillations. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (pp.134,137) unstable focus http://identifiers.org/isbn/0198565623 (p.25) unstable spiral point http://identifiers.org/isbn/0198565623 (p.73) TEDDY_0000128 unstable limit cycle http://identifiers.org/isbn/0738204536 If all trajectories [http://identifiers.org/teddy/TEDDY_0000083] that start near the limit cycle [http://identifiers.org/teddy/TEDDY_0000051] (both inside and outside) spiral outward, then the limit cycle is called unstable. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.196) TEDDY_0000129 unstable fixed point http://identifiers.org/isbn/0738204536 A fixed point [http://identifiers.org/teddy/TEDDY_0000086] which is not Liapunov stable [not TEDDY_0000113]. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.17) TEDDY_0000130 inflexion point http://mathworld.wolfram.com/InflectionPoint.html An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local maxima or local minima. http://mathworld.wolfram.com/InflectionPoint.html Weisstein, Eric W. Inflection Point. From MathWorld--A Wolfram Web Resource. TEDDY_0000131 amplitude http://mathworld.wolfram.com/Amplitude.html A magnitude of an oscillation. http://mathworld.wolfram.com/Amplitude.html Weisstein, Eric W. "Amplitude." From MathWorld--A Wolfram Web Resource. TEDDY_0000132 behaviour diversification Behaviour diversification describes the way one or several temporal behaviours [http://identifiers.org/teddy/TEDDY_0000083] are modified or related upon interaction with information external to the system considered. TEDDY_0000133 Lyapunov stability http://identifiers.org/isbn/0198565623 Liapunov stability solution stability A solution x*(t) of the n-dimentional system x ̇=X(x, t) is Liapunov stable, if no matter how small is the permitted deviation, measured by epsilon, there still exists a nonzero tolerance, measured by delta, in the initial conditions when the system is activated, allowing it to run satisfactorily. http://identifiers.org/isbn/0198565623 Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.286) solution stability http://identifiers.org/isbn/0198565623 (p.286) TEDDY_0000134 half-stability http://identifiers.org/isbn/0738204536 An invariant set is called half-stable if there exist a stable and an unstable manifold with respect to the invariant set. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.26,196) TEDDY_0000135 only local stability http://identifiers.org/isbn/0738204536 An asymptotically stable [http://identifiers.org/teddy/TEDDY_0000097] behaviour [http://identifiers.org/teddy/TEDDY_0000083] to which only behaviours starting in a restricted neighbourhood will converge. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.20) TEDDY_0000136 global stability http://identifiers.org/isbn/0738204536 An asymptotically stable [http://identifiers.org/teddy/TEDDY_0000097] behaviour [http://identifiers.org/teddy/TEDDY_0000083] to which all other behaviours will converge independent of the initial distance. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.20) TEDDY_0000137 stable node http://identifiers.org/isbn/0738204536 nodal sink A fixed point node [http://identifiers.org/teddy/TEDDY_0000087] which is stable [http://identifiers.org/teddy/TEDDY_0000133], i.e. for which the Jacobian matrix has two negative eigenvalues. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137) TEDDY_0000138 unstable node http://identifiers.org/isbn/0738204536 nodal source A fixed point node [http://identifiers.org/teddy/TEDDY_0000087] which is unstable [not TEDDY_0000133], i.e. for which the Jacobian matrix has two positive eigenvalues. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137) TEDDY_0000139 stable star http://identifiers.org/isbn/0738204536 stable proper node A star [http://identifiers.org/teddy/TEDDY_0000090] which is stable [http://identifiers.org/teddy/TEDDY_0000133], i.e. for which the Jacobian matrix has two identical negative eigenvalues. All other trajectories [http://identifiers.org/teddy/TEDDY_0000083] of the system are straight lines towards the fixed point. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137) TEDDY_0000140 unstable star http://identifiers.org/isbn/0738204536 unstable proper node A star [http://identifiers.org/teddy/TEDDY_0000090] which is unstable [not TEDDY_0000133], i.e. for which the Jacobian matrix has two identical positive eigenvalues. All other trajectories [http://identifiers.org/teddy/TEDDY_0000083] of the system are straight lines away the fixed point. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137) TEDDY_0000141 stable degenerate node http://identifiers.org/isbn/0738204536 degenerate stable node stable degenerated node stable improper node A degenerated node [http://identifiers.org/teddy/TEDDY_0000093] which is stable [http://identifiers.org/teddy/TEDDY_0000133], i.e. for which the Jacobian matrix has two identical negative eigenvalues. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137) degenerate stable node http://identifiers.org/isbn/0198565623 (p.73) TEDDY_0000142 unstable degenerate node http://identifiers.org/isbn/0738204536 degenerate unstable point unstable degenerated node unstable improper node A degenerated node [http://identifiers.org/teddy/TEDDY_0000093] which is unstable [not TEDDY_0000133], i.e. for which the Jacobian matrix has two identical positive eigenvalues. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137) degenerate unstable point http://identifiers.org/isbn/0198565623 (p.73) TEDDY_0000143 non-periodic orbit http://identifiers.org/isbn/9781402014031 A 'temporal behaviour' [http://identifiers.org/teddy/TEDDY_0000083] which never repeats its state. http://identifiers.org/isbn/9781402014031 Coley AA. (2003) Dynamical systems and cosmology, Kluwer Academic Publishers, Dordrecht. (p.10) TEDDY_0000144 monotonicity characteristic A characteristic describing the order of the successive states of a curve. TEDDY_0000145 half-stable limit cycle http://identifiers.org/isbn/0738204536 semi-stable limit cycle semistable limit cycle If trajectories [http://identifiers.org/teddy/TEDDY_0000083] on one side of the limit cycle [http://identifiers.org/teddy/TEDDY_0000051] spiral inward and on the other side spiral outward, it is called semistable. http://identifiers.org/isbn/0738204536 Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.196) semi-stable limit cycle http://identifiers.org/isbn/0198565623 (p.114) TEDDY_0000146 asymptotic behaviour A `temporal behaviour` [http://identifiers.org/teddy/TEDDY_0000083] which converges to some `limit behaviour` [http://identifiers.org/teddy/TEDDY_0000085]. TEDDY_0000147 global bifurcation http://identifiers.org/isbn/0387983821 A bifurcation [http://identifiers.org/teddy/TEDDY_0000053] in which at least two limit cycles [http://identifiers.org/teddy/TEDDY_0000051] or fixed points TEDDY_0000086 are involved. It can not be detected within a small neighborhood of a fixed point. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.59) TEDDY_0000148 stability characteristic A characteristic describing stability of a 'temporal behaviour' [http://identifiers.org/teddy/TEDDY_0000083], i.e. how far from each other solutions with close initial states become as time passes. TEDDY_0000149 Poincaré stability http://identifiers.org/isbn/0198565623 Poisson stability orbitally stable behaviour The solution x*(t), t >= t0 is Poincaré stable, if all sufficiently small disturbances of the initial value a* lead to half-paths remaining for all later time at a small distance from the half-path H* with initial point a*. http://identifiers.org/isbn/0198565623 Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.278) Poisson stability http://identifiers.org/isbn/0821803670 orbitally stable behaviour http://identifiers.org/isbn/0198565623 (p.278) TEDDY_0000150 uniform stability http://identifiers.org/isbn/0198565623 A Liapunov stable [http://identifiers.org/teddy/TEDDY_0000133] solution [http://identifiers.org/teddy/TEDDY_0000083] is uniformly stable if its sensitivity to disturbance does not increase indefinitely with time. http://identifiers.org/isbn/0198565623 Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.288) 2 TEDDY_0000151 heteroclinic orbit http://identifiers.org/isbn/0198565623 heteroclinic path A heteroclinic orbit is a trajectory [http://identifiers.org/teddy/TEDDY_0000083] of a dynamical system that tends to two different invariant sets as time approaches positive and negative infinities. http://identifiers.org/isbn/0198565623 Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (pp.114-115) heteroclinic path http://identifiers.org/isbn/0198565623 (pp.114-115) 1 TEDDY_0000152 homoclinic orbit http://identifiers.org/isbn/0198565623 homoclinic path A homoclinic orbit is a trajectory [http://identifiers.org/teddy/TEDDY_0000083] of a dynamical system that tends to the same invariant set as time approaches positive and negative infinities. http://identifiers.org/isbn/0198565623 Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (pp.114-115) homoclinic path http://identifiers.org/isbn/0198565623 (pp.114-115) TEDDY_0000153 heteroclinic bifurcation http://identifiers.org/isbn/0387983821 A global bifurcation [http://identifiers.org/teddy/TEDDY_0000147] in which two saddles [http://identifiers.org/teddy/TEDDY_0000089] are only connected at the bifurcation point by a heteroclinic saddle connection [http://identifiers.org/teddy/TEDDY_0000101]. This saddle connection does not exist below and above the bifurcation. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.59) TEDDY_0000154 homoclinic bifurcation http://identifiers.org/isbn/0387983821 saddle-loop bifurcation A global bifurcation [http://identifiers.org/teddy/TEDDY_0000147] in which a homoclinic saddle connection [http://identifiers.org/teddy/TEDDY_0000100] only exists at the bifurcation point. There exists a Limit Cycle [http://identifiers.org/teddy/TEDDY_0000051] either below or above the bifurcation. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.200ff) saddle-loop bifurcation http://identifiers.org/isbn/0738204536 (p.263) TEDDY_0000157 hyperbolicity http://identifiers.org/isbn/0198565623 http://identifiers.org/isbn/0387983821 A fixed point [http://identifiers.org/teddy/TEDDY_0000086] is said to be hyperbolic if all eigenvalues of the Jacobian matrix have non-zero real parts. A limit cycle [http://identifiers.org/teddy/TEDDY_0000051] is called hyperbolic if the fixed point of the Poincare ́map is hyperbolic. http://identifiers.org/isbn/0198565623 Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.74) http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.55) TEDDY_0000162 two-node positive feedback loop http://identifiers.org/isbn/1584886420 2-node positive feedback 2-node positive feedback loop two-node positive feedback A network motif in which two transcription factors regulate each other with the regulation signs of the two interactions leading to a positive feedback loop. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.99) TEDDY_0000163 double-positive feedback loop http://identifiers.org/isbn/1584886420 double-positive feedback A positive feedback loop made of two positive interactions, so that the two transcription factors activate each other. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.99) TEDDY_0000164 double-negative feedback loop http://identifiers.org/isbn/1584886420 double-negative feedback A positive feedback loop made of two negative interactions, so that the two transcription factors repress each other. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.99) TEDDY_0000165 multi-output feed-forward loop http://identifiers.org/isbn/1584886420 multi-output FFL A simple topological generalization of the 'three-node feed-forward loop' [http://identifiers.org/teddy/TEDDY_0000037] based on multiplication of the output node. http://identifiers.org/isbn/1584886420 Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.83) TEDDY_0000166 toggle switch http://identifiers.org/pubmed/10659857 A two-node double-negative loop. http://identifiers.org/pubmed/10659857 Gardner TS, Cantor CR, Collins JJ (2000) Construction of a genetic toggle switch in Escherichia coli, Nature; 403(6767):339-42. TEDDY_0000167 structural stability http://identifiers.org/isbn/0387983821 Andronov's structural stability A system x ̇=f(x), x ∈ Rn (1), defined in a region D ⊂ Rn is called structurally stable in a region D0 ⊂ D if for any sufficiently C1-close in D system x ̇=g(x), x ∈ Rn (2), there are regions U, V ⊂ D, D0 ⊂ U such that (1) is topologically equivalent in U to (2) in V. http://identifiers.org/isbn/0387983821 Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.71) TEDDY_0000175 regular attractor http://identifiers.org/isbn/9810221428 simple attractor The attractor [http://identifiers.org/teddy/TEDDY_0000094] is regular or simple if the phase trajectories [http://identifiers.org/teddy/TEDDY_0000083] on the attractor are stable according both to Lyapunov [http://identifiers.org/teddy/TEDDY_0000113] and to Poisson [http://identifiers.org/teddy/TEDDY_0000149]. http://identifiers.org/isbn/9810221428 V. S. Anishchenko (1995) Dynamical Chaos-Models and Experiments: Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific Series on Nonlinear Science, Series a, Vol 8). World Scientific Pub Co Inc. (p.10) TEDDY_0000177 blue sky catastrophe A 'bifurcation of limit cycle' [http://identifiers.org/teddy/TEDDY_0000070] in which a limit cycle collides with a non-hyperbolic cycle. TEDDY_0000178 curve quantitative characteristic A quantitative characteristic of the graph of a function. TEDDY_0000179 excitability http://identifiers.org/doi/10.1142/S0218127400000840 http://identifiers.org/pubmed/16333295 According to the intuitive definition of excitability, small perturbations near the equilibrium can cause large excursions for the solution before it returns to the equilibrium. http://identifiers.org/doi/10.1142/S0218127400000840 Eugene M. Izhikevich: Neural Excitability, Spiking and Bursting. Int. J. Bifurcation Chaos, 10, 1171 (2000). http://identifiers.org/pubmed/16333295 Tyson JJ.: Modeling the cell division cycle: cdc2 and cyclin interactions. Proc Natl Acad Sci U S A. 1991 Aug 15;88(16):7328-32. TEDDY_obsolete _obsolete true rel-2014-04-24 (inferred) en The TErminology for the Description of DYnamics (TEDDY) project aims to provide an ontology for dynamical behaviours, observable dynamical phenomena, and control elements of bio-models and biological systems in Systems Biology and Synthetic Biology. TErminology for the Description of DYnamics (TEDDY) http://co.mbine.org/specifications/teddy http://teddyontology.svn.sourceforge.net/svnroot/teddyontology/teddy/tags/rel-2011-08-30/teddy.owl rel-2014-04-24 (inferred) hasPart Inverse of partOf [obo:part_of]. http://identifiers.org/isbn/9810221428 (p.10) http://identifiers.org/isbn/9810221428 (p.10) http://identifiers.org/isbn/0387983821 (p.196) 3 1 2