]>
http://teddyontology.sourceforge.net/
http://teddyontology.svn.sourceforge.net/svnroot/teddyontology/teddy/tags/rel-2007-09-03/ontology/teddy.owl
TErminology for the Description of DYnamics (TEDDY)
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.
rel-2009-10-16
SVN: $HeadURL: https://teddyontology.svn.sourceforge.net/svnroot/teddyontology/teddy/trunk/ontology/teddy.owl $
$Revision: 185 $ $Date: 2009-10-16 09:09:12 +0200 (Fr, 16. Okt 2009) $
$Author: tral $
hasCharacteristic
This relation is used to describe properties of a Temporal Behaviour by means of Behaviour Characteristic.
hasPart
hasSubPart
partOf
hasSuperPart
hasOnPart
This relation describes the Stability of a Temporal Behaviour.
hasStability
Two Temporal Behaviours are adjacentTo each other if and only if they are in phase space proximity.
adjacentTo
A Temporal Behaviour convergeTo another Temporal Behaviour if and only if it reaches the other Behaviour as time goes to either positive or negative infinity.
convergeTo
hasValue
A TEDDY Entity is 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 Entity
Curve ((obsolete))
Obsolete: equivalent to TEDDY_0000083 "Temporal Behaviour".
Behaviour Characteristic
Functional Motif
A curve is ``Monotonic'' if successive states are orderd either entirely non-decreasing or entirely non-increasing.
http://mathworld.wolfram.com/MonotonicFunction.html
Monotonic
A curve is Non-Monotonic if it has both increasing ordered successive states and decreasing orderd succesive states.
Non-Monotonic
Oscillating
A curve is Strictly Monotonic if it is Monotonic and has no equal temporal successive states.
Strictly Monotonic
A curve is Strictly Increasing if it is Strictly Monotonic with temporal successive states increasing ordered.
Strictly Increasing (Isotonic)
A curve is Strictly Decreasing if it is Strictly Monotonic with temporal successive states decreasing ordered.
Strictly Decreasing (Antitonic)
Single Turnaround
Obsolete: equivalent to TEDDY_0000086 "Fixed Point".
Steady State ((obsolete))
Growth
Linear Growth
Exponential Growth
Curve Shape
Concave Shape
Zero Growth
Polynomial Growth
Linear Increasing
Linear Decreasing
Convex Shape
Straight Line Shape
Curve Characteristic
Unbounded Growth
Limit
Asymptotic Limit
Asymptotic Upper Limit
Asymptotic Lower Limit
Plus Infinity Limit
Infinite Limit
Minus Infinity Limit
Sigmoid Shape
Feedback
Negative Feedback
Positive Feedback
Feedforward
3-node Feedforward
Coherent 3-node Feedforward
C1-FFL
Coherent 3-node Feedforward Type-1
C2-FFL
Coherent 3-node Feedforward Type-2
C3-FFL
Coherent 3-node Feedforward Type-3
C4-FFL
Coherent 3-node Feedforward Type-4
Incoherent 3-node Feedforward
I1-FFL
Incoherent 3-node Feedforward Type-1
I2-FFL
Incoherent 3-node Feedforward Type-2
I3-FFL
Incoherent 3-node Feedforward Type-3
I4-FFL
Incoherent 3-node Feedforward Type-4
Orbit ((obsolete))
Obsolete: equivalent to TEDDY_0000083 "Temporal Behaviour".
Fixed Point ((obsolete))
Obsolete: equivalent to TEDDY_0000086 "Fixed Point".
urn:miriam:isbn:0387983821 (p.9)
Periodic Solution
Closed Orbit
A Periodic Orbit is a Temporal Behaviour which repeats every state after a specific period of time.
Periodic Orbit
Cycle
German synonym Grenzzyklus: ISBN 3817112823
Limit Cycle
Grenzzyklus
urn:miriam:isbn:0738204536 (p.196)
A Limit Cycle is a Closed Orbit which is isolated, i.e. neighbouring Orbits are not closed.
Parameter Dependency ((obsolete))
Obsolete: not required anymore.
1
1
A ``Bifurcation'' is a ``Characteristic'' describing a qualitative (topological) change in the orbit structure of a system.
Bifurcation
http://www.egwald.com/nonlineardynamics/bifurcations.php
A Strange Attractor is an Non-Periodic Orbit which is Attracting and exhibits sensitive dependence on initial conditions.
Chaotic Attractor
Fractal Attractor
Strange Attractor
Synonyms "Chaotic Attractor", "Fractal Attractor": urn:miriam:isbn:0738204536 (p.325)
urn:miriam:isbn:0738204536 (p.325)
Bursting
Switch
Stability
urn:miriam:isbn:3817112823 (p.53)
Stability is a Behaviour Characteristic describing behaviours starting near the characterised behaviour. The "nearness" between behaviours requires an appropriate metric.
Asymptotic Decreasing
Asymptotic Increasing
Diverging Increasing
Non-Periodically Oscillating
Obsolete: equivalent to TEDDY_0000051 "Limit Cycle".
Sustained Oscillation ((obsolete))
Damped Oscillating
Single-Periodically Oscillating
Mixed-Mode Oscillating
Periodically Oscillating
Period
Regularity ((obsolete))
Obsolete: not required anymore.
A ``Local Bifurcation'' is a ``Bifurcation'' in which a ``Stable Fixed Point'' changes to an unstable 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.
Bifurcation from Steady State (EP)
Bifurcation of Equilibrium
Bifurcation of Fixed Point
Local Bifurcation
http://en.wikipedia.org/wiki/Bifurcation_theory#Local_bifurcations
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.58
synonym "Bifurcation from Steady State (EP)": http://www.scholarpedia.org/article/MATCONT
synonyms "Bifurcation of Equilibrium", "Bifurcation of Fixed Point": http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.58
Bifurcation from Limit Cycle
A ``Saddle-Node Bifurcation'' is a ``Zero-Eigenvalue Bifurcation'' in which a ``Stable Fixed Point'' and an ``Unstable Fixed Point'' collide and mutually annihilate.
Blue Sky Bifurcation
Fold Bifurcation
Limit Point Bifurcation
Saddle-Node Bifurcation
Tangent Bifurcation
Turning-Point Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.80
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.45
synonym "Limit Point Bifurcation": http://www.scholarpedia.org/article/Saddle-node_Bifurcation
synonym "Tangent Bifurcation": http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.80
synonyms "Fold Bifurctaion", "Turning-Point Bifurcation", "Blue Sky Bifurcation": http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.47
A ``Hopf Bifurcation'' is a ``Local Bifurcation'' in which a ``Stable Spiral'' changes in an ``Unstable Spiral''. The linearisation around the fixed point has two conjugate eigenvalues. This eigenvalues cross simultaneously the imaginary axis from left (negative real part) to the right during the bifurcation.
Andronov-Hopf Bifurcation
Hopf Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.248ff
synonym "Andronov-Hopf Bifurcation": http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.80
A ``Subcritical Hopf Bifurcation'' is a ``Hopf Bifurcation'' in which an ``Unstable Limit Cycle'' is destroyed.
Subcritical Andronov-Hopf Bifurcation (Subc-AH)
Subcritical Hopf Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.88
synonym "Subcritical Andronov-Hopf Bifurcation (Subc-AH)": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
A ``Supercritical Hopf Bifurcation'' is a ``Hopf Bifurcation'' in which an ``Stable Limit Cycle'' appears.
Supercritical Andronov-Hopf Bifurcation (Supc-AH)
Supercritical Hopf Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.249
synonym "Supercritical Andronov-Hopf Bifurcation (Supc-AH)": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
SNIC
Saddle-Node on Invariant Circle Bifurcation
synonym "SNIC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
SNLC
Saddle-Node Bifurcation of Limit-Cycles
synonym "SNLC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
PDLC
Period-Doubling Bifurcation of Limit-Cycles
synonym "PDLC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
NSLC
Neimark-Sacker Bifurcation of Limit-Cycles
synonym "NSLC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
Integrator
_obsolete Behaviour ((obsolete))
Obsolete: only one obsolete branch required.
_obsolete Characteristic ((obsolete))
Obsolete: only one obsolete branch required.
_obsolete Functionality ((obsolete))
Obsolete: only one obsolete branch required.
Temporal Behaviour
A Temporal Behaviour is a temporal sequence of states following the evolution operator of the dynamical system through a given initial state.
Synonyms: Orbit (urn:miriam:isbn:0387983821 p.8), Trajectory (urn:miriam:isbn:0387983821 p.8), Solution Curve (urn:miriam:isbn:0387908196 p.2)
Solution Curve
Trajectory
urn:miriam:isbn:0387983821 (p.8)
Phase Curve
Orbit
Parametrical Behaviour ((obsolete))
Obsolete: not required anymore.
Asymptotic Behaviour
An Asymptotic Behaviour is a Temporal Behaviour to which behaviours starting nearby tend as time goes to either positive or negative infinity.
Asymptotic State
urn:miriam:isbn:0387983821 (p.10)
Limit Set
Fixed Point
http://mathworld.wolfram.com/FixedPoint.html
Constant Behaviour
Equilibrium Point
Critical Point
A Fixed Point is a Temporal Behaviour which does not change its state.
Constant Solution
Steady State
Rest Solution
Equilibrium
A Fixed Point Node is a Fixed Point for which the Jacobian matrix has real-valued eigenvalues of the same sign.
Fixed Point Node
urn:miriam:isbn:0738204536 (p.137)
Center
A Center is a Fixed Point 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.
Elliptic Fixed Point
urn:miriam:isbn:0738204536 (p.134,137)
Saddle Point
urn:miriam:isbn:0738204536 (p.137)
A Saddle Point is a Fixed Point for which the Jacobian matrix has real-valued eigenvalues of opposite signs.
Is also called ''Hyperbolic Fixed Point'' (http://mathworld.wolfram.com/HyperbolicFixedPoint.html), but ''Hyperbolic Fixed Point'' is also used for ''Non-Elliptic Fixed Point'', i.e. eigenvalues are not purely imaginary (References#strogatz00, p.155; http://www.egwald.ca/nonlineardynamics/twodimensionaldynamics.php#topologicalclassification).
urn:miriam:isbn:0738204536 (p.135)
A Star is a Fixed Point for which the Jacobian Matrix has identical eigenvalues and two independent corresponding eigenvectors. All other trajectories of the system lie on straight through the Fixed Point.
Star
A Spiral Point is a Fixed Point for which the Jacobian matrix has not purely imaginary complex conjugate eigenvalues. The Fixed Point is surrounded by spiralling behaviours.
Spiral Point
urn:miriam:isbn:0738204536 (p.134,137)
Non-isolated Fixed Point
urn:miriam:isbn:0738204536 (p.128,137)
A Non-Isolated Fixed Point is a Fixed Point 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.
Degenerated Node
urn:miriam:isbn:0738204536 (p.135f)
A Degenerated Node is a Fixed Point for which the Jacobian Matrix has identical eigenvalues and only one independent eigenvector. All other trajectories of the system asymptotically become parallel to the unique eigendirection.
Improper Node
Attractor
An '''Attractor''' is an ''Asymptotic Behaviour'' to which all neighboring trajectories converge.
ISBN 0738204536 (p.324)
Liapunov Stable Fixed Point
urn:miriam:isbn:0738204536 (p.129)
A Liapunov Stable Fixed Point is a Fixed Point which is Liapunov Stable.
A Behaviour is Unstable if it is neither Liapunov Stable nor Attracting.
Repelling
Unstable
urn:miriam:isbn:0738204536 (p.129)
A Behaviour is Stable if it is Liapunov Stable and Attracting.
Asymptotically Stable
Stable
urn:miriam:isbn:0738204536 (p.129)
A Behaviour is Neutrally Stable if it is Liapunov Stable and not Attracting.
Neutrally Stable
urn:miriam:isbn:0738204536 (p.129)
1
2
urn:miriam:isbn:0738204536 (p.184)
Saddle Connection
A Saddle Connection is a Temporal Behaviour connecting two Saddle Points.
1
Homoclinic Orbit
Homoclinic Loop
urn:miriam:isbn:0738204536 (p.161)
A Homoclinic Orbit is a Saddle Connection connecting a Saddle Point to itself.
Saddle Loop
Synonyms: Homoclinic Loop (urn:miriam:isbn:3540971416 p.213), Saddle Loop (http://www.egwald.ca/nonlineardynamics/mathappendix.php#limitset)
2
Heteroclinic Orbit
The term ''Saddle Connection'' is used as a synonym for a heteroclinic orbit (urn:miriam:isbn:0738204536 (p.166) ). But ''Saddle Connection'' is also used for both: homoclinic and heteroclinic orbits (urn:miriam:isbn:0387943773 (p.184)).
Synonyms: Heteroclinic Trajectory (urn:miriam:isbn:0738204536 p.166)
A Heteroclinic Orbit is a Saddle Connection connecting two different Saddle Points.
Heteroclinic Trajectory
urn:miriam:isbn:0738204536 (p.166)
A ``Repeller'' is a ``repelling'' ``Asymptotic Behaviour''.
Repeller
Unstable Behaviour
A Behaviour is Attracting if all behaviours starting sufficiently near to the set will approach it.
Attracting
urn:miriam:isbn:0738204536 (p.128)
Half-Stable Fixed Point
A Half-Stable Fixed Point is an one-dimensional Fixed Point which is Half-Stable, i.e. the Fixed Point is Attracting in one direction and Unstable in the other direction.
urn:miriam:isbn:0738204536 (p.26)
Neutrally Stable Behaviour
A Neutrally Stable Behaviour is a Temporal Behaviour which is neither Attracting nor Unstable.
urn:miriam:isbn:0738204536 (p.129)
Non-Isolated Asymptotic Behaviour
A Non-Isolated Cycle is a Cycle which is surrounded by other Cycles.
urn:miriam:isbn:0738204536 (p.196)
Non-Isolated Cycle
Neutrally Stable Cycle
Temporal Behaviour ((obsolete))
Obsolete: equivalent to TEDDY_0000083 "Temporal Behaviour".
A ``Perturbation Behaviour'' is a ``Behaviour'' with respect to perturbations of the system or its environment.
Perturbation Behaviour
A ``Stable Behaviour'' is a ``Perturbation Behaviour'' shown by a system with a single ``Attractor''. For all initial states sufficiently near to the attractor the system tend to this attractor.
Stable Behaviour
2
A ``Bistable Behaviour'' is a ``Perturbation Behaviour'' shown by a system with two different ``Attractor''s. Depending on the initial state the system tend to the one or the other attractor.
Bistable Behaviour
3
A ``Multistable Behaviour'' is a ``Perturbation Behaviour'' shown by a system with more than two different ``Attractor''s. Depending on the initial state the system tend to one of the attractors.
Multistable Behaviour
Quasiperiodic Oscillating
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.276
http://www.scholarpedia.org/article/Quasiperiodic_oscillations
Stable Fixed Point
Attractor
A Stable Fixed Point is a Fixed Point which is Stable.
urn:miriam:isbn:0738204536 (p.17)
Sink
Stable Limit Cycle
A Stable Limit Cycle is a Limit Cycle which is Stable.
urn:miriam:isbn:0738204536 (p.196)
Neutrally Stable Fixed Point
A Neutrally Stable Fixed Point is a Fixed Point which is Neutrally Stable.
urn:miriam:isbn:0738204536 (p.129)
1
Magnitude
High Magnitude
Low Magnitude
Infinite-Period Bifurcation
Saddle-Node Homoclinic Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.59ff
synonym "Infinite-Period Bifurcation": http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.262
A ``Degenerate Hopf Bifurcation'' is a ``Hopf Bifurcation'' in which neigther a Limit Cycle is destroyed nor a Limit Cycle appears. On the bifurcation the fixed point is a ``Center''.
Degenerate Hopf Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.253
A ``Transcritical Bifurcation'' is a ``Zero-Eigenvalue Bifurcation'' in which a ``Stable Fixed Point'' and an ``Unstable Fixed Point'' coalesce and exchange their stability.
Transcritical Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.50f
A ``Pitchfork Bifurcation'' is a ``Zero-Eigenvalue Bifurcation'' in which the fixed point is surrounded by two symmetrical fixed points on one side of the bifurcation.
Pitchfork Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.55
A ``Zero-Eigenvalue Bifurcation'' is a ``Local Bifurcation'' in which one of the eigenvalue of the linarisation around the fixed point is zero at the bifurcation.
Zero-Eigenvalue Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.248
A ``Subcritical Pitchfork Bifurcation'' is a ``Pitchfork Bifurcation'' in which two symmetrical ``Unstable Fixed Points'' collide with the stable fixed point and disappear.
Subcritical Pitchfork Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.58f
A ``Supercritical Pitchfork Bifurcation'' is a ``Pitchfork Bifurcation'' in which two symmetrical ``Stable Fixed Points'' appear from the stable fixed point.
Supercritical Pitchfork Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.55f
A Stable Spiral Point is a Spiral Point which is Stable, i.e. for which the Jacobian Matrix has two negative complex conjugate eigenvalues. The Fixed Point is surrounded by behaviours spiralling downward the Fixed Point, corresponding to decaying oscillations.
urn:miriam:isbn:0738204536 (p.134,137)
Stable Spiral Point
An Unstable Spiral Point is a Spiral Point which is Unstable, i.e. for which the Jacobian Matrix has two positive complex conjugate eigenvalues. The Fixed Point is surrounded by behaviours spiralling upward the Fixed Point, corresponding to growing oscillations.
Unstable Spiral Point
urn:miriam:isbn:0738204536 (p.134,137)
Unstable Limit Cycle
An Unstable Limit Cycle is a Limit Cycle which is Unstable.
urn:miriam:isbn:0738204536 (p.196)
Unstable Fixed Point
urn:miriam:isbn:0738204536 (p.17)
Source
Repeller
An Unstable Fixed Point is a Fixed Point which is Unstable.
Inflexion Point
Amplitude
Behaviour Diversification
A Behaviour is Liapunov Stable if all behaviours starting sufficiently near to the set remain close to it.
urn:miriam:isbn:0738204536 (p.129)
Liapunov Stable
An one-dimensional Fixed Point is Half-Stable if it is Attracting in one direction and Unstable in the other direction. A two-dimensional Limit Cycle is Half-Stable if it is Attracting outside and Unstable inside or vice versa.
Half-Stable
urn:miriam:isbn:0738204536 (p.26,196)
A Behaviour is Only Locally Stable if it is Stable, but only behaviours starting in a restricted neighbourhood will approach it.
Only Locally Stable
urn:miriam:isbn:0738204536 (p.20)
Globally Stable
A Behaviour is Globally Stable if it is Stable and all other behaviours will approach it.
urn:miriam:isbn:0738204536 (p.20)
A Stable Node is a Fixed Point Node which is Stable, i.e. for which the Jacobian Matrix has two negative eigenvalues.
urn:miriam:isbn:0738204536 (p.137)
Stable Node
An Unstable Node is a Fixed Point Node which is Unstable, i.e. for which the Jacobian Matrix has two positive eigenvalues.
urn:miriam:isbn:0738204536 (p.137)
Unstable Node
urn:miriam:isbn:0738204536 (p.137)
A Stable Star is a Star which is Stable, i.e. for which the Jacobian Matrix has two identical negative eigenvalues. All other trajectories of the system are straight lines towards the Fixed Point.
Stable Star
Unstable Star
urn:miriam:isbn:0738204536 (p.137)
An Unstable Star is a Star which is Unstable, i.e. for which the Jacobian Matrix has two identical positive eigenvalues. All other trajectories of the system are straight lines away the Fixed Point.
Stable Improper Node
urn:miriam:isbn:0738204536 (p.137)
A Stable Degenerated Node is a Degenerated Node which is Stable, i.e. for which the Jacobian Matrix has two identical negative eigenvalues.
Stable Degenerated Node
Unstable Improper Node
Unstable Degenerated Node
urn:miriam:isbn:0738204536 (p.137)
An Unstable Degenerated Node is a Degenerated Node which is Unstable, i.e. for which the Jacobian Matrix has two identical positive eigenvalues.
Non-Periodic Orbit
urn:miriam:isbn:9781402014031 (p.10)
A Non-Periodic Orbit is a Temporal Behaviour which never repeats a state.
Monotonicity
urn:miriam:isbn:0738204536 (p.196)
A Half-Stable Limit Cycle is a Limit Cycle which is Half-Stable, i.e. the Limit Cycle is Attracting outside and Unstable inside or vice versa.
Half-Stable Limit Cycle
_obsolete
en