]>
TErminology for the Description of DYnamics (TEDDY)
http://teddyontology.sourceforge.net/
https://teddyontology.svn.sourceforge.net/svnroot/teddyontology/teddy/tags/rel-2009-10-16/ontology/teddy.owl
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-2011-03-10 (inferred)
classified by HermiT 1.3.3
hasCharacteristic
Used to describe properties of a Temporal Behaviour by means of Behaviour Characteristic.
hasPart
hasSubPart
partOf
hasSuperPart
hasOnPart
Two Temporal Behaviours are adjacentTo each other if and only if they are in phase space proximity.
adjacentTo
convergeTo
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.
hasValue
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
Obsolete: equivalent to TEDDY_0000083 'Temporal Behaviour'.
curve ((obsolete))
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'.
A Temporal Behaviour which repeats every state after a specific period of time.
Periodic Solution
Closed Orbit
Cycle
periodic orbit
urn:miriam:isbn:0387983821 (p.9)
German synonym Grenzzyklus: ISBN 3817112823
limit cycle
Grenzzyklus
A Closed Orbit which is isolated, i.e. neighbouring Orbits are not closed.
urn:miriam:isbn:0738204536 (p.196)
parameter dependency ((obsolete))
Obsolete: not required anymore.
1
1
A `characteristic` describing a qualitative (topological) change in the orbit structure of a system.
bifurcation
http://www.egwald.com/nonlineardynamics/bifurcations.php
An Non-Periodic Orbit which is Attracting and exhibits sensitive dependence on initial conditions.
Chaotic Attractor
Fractal Attractor
Synonyms 'Chaotic Attractor', 'Fractal Attractor': urn:miriam:isbn:0738204536 (p.325)
strange attractor
urn:miriam:isbn:0738204536 (p.325)
bursting
switch
stability ((obsolete))
Obsolete: not required anymore.
asymptotic decreasing
asymptotic increasing
diverging increasing
non-periodically oscillating
sustained oscillation ((obsolete))
Obsolete: equivalent to TEDDY_0000051 'Limit Cycle'.
damped oscillating
single-periodically oscillating
mixed-mode oscillating
periodically oscillating
period
regularity ((obsolete))
Obsolete: not required anymore.
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
http://en.wikipedia.org/wiki/Bifurcation_theory#Local_bifurcations
local bifurcation
synonym 'Bifurcation from Steady State (EP)': http://www.scholarpedia.org/article/MATCONT
synonyms 'Bifurcation of Equilibrium', 'Bifurcation of Fixed Point': urn:miriam:isbn:0387983821 (p.58)
urn:miriam:isbn:0387983821 (p.58)
bifurcation from limit cycle
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
Tangent Bifurcation
Turning-Point Bifurcation
saddle-node bifurcation
synonym 'Limit Point Bifurcation': http://www.scholarpedia.org/article/Saddle-node_Bifurcation
synonym 'Tangent Bifurcation': urn:miriam:isbn:0387983821 (p.80)
synonyms 'Fold Bifurctaion', 'Turning-Point Bifurcation', 'Blue Sky Bifurcation': urn:miriam:isbn:0738204536 (p.47)
urn:miriam:isbn:0387983821 (p.80)
urn:miriam:isbn:0738204536 (p.45)
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
synonym 'Andronov-Hopf Bifurcation': urn:miriam:isbn:0387983821 (p.80)
urn:miriam:isbn:0738204536 (p.248ff)
A `hopf bifurcation` in which an `unstable limit cycle` is destroyed.
Subcritical Andronov-Hopf Bifurcation (Subc-AH)
subcritical hopf bifurcation
synonym 'Subcritical Andronov-Hopf Bifurcation (Subc-AH)': http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
urn:miriam:isbn:0387983821 (p.88)
A `hopf bifurcation` in which an `stable limit cycle` appears.
Supercritical Andronov-Hopf Bifurcation (Supc-AH)
supercritical hopf bifurcation
synonym 'Supercritical Andronov-Hopf Bifurcation (Supc-AH)': http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
urn:miriam:isbn:0738204536 (p.249)
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
Phase Curve
Solution Curve
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)
Orbit
Trajectory
urn:miriam:isbn:0387983821 (p.8)
parametrical behaviour ((obsolete))
Obsolete: not required anymore.
limit behaviour
urn:miriam:isbn:0387983821 (p.10)
A `temporal behaviour` [TEDDY_0000083] with all behaviours starting sufficiently near converge to it as time goes to either positive or negative infinity.
Asymptotic State
Limit Set
fixed point
http://mathworld.wolfram.com/FixedPoint.html
Rest Solution
Equilibrium
A Temporal Behaviour which does not change its state.
Equilibrium Point
Constant Solution
Steady State
Constant Behaviour
Critical Point
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 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.
urn:miriam:isbn:0738204536 (p.134,137)
Elliptic Fixed Point
saddle point
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.137)
A Fixed Point for which the Jacobian matrix has real-valued eigenvalues of opposite signs.
star
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.
urn:miriam:isbn:0738204536 (p.135)
spiral point
urn:miriam:isbn:0738204536 (p.134,137)
A Fixed Point for which the Jacobian matrix has not purely imaginary complex conjugate eigenvalues. The Fixed Point is surrounded by spiralling behaviours.
non-isolated fixed point
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.
urn:miriam:isbn:0738204536 (p.128,137)
degenerated node
urn:miriam:isbn:0738204536 (p.135f)
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 `asymptotic behaviour` to which all neighboring trajectories converge.
ISBN 0738204536 (p.324)
liapunov stable fixed point
urn:miriam:isbn:0738204536 (p.129)
A Fixed Point which is Liapunov Stable.
A `limit behaviour` which it is neither a `Liapunov stable behaviour` nor a `stable behaviour`.
Repeller
unstable behaviour
urn:miriam:isbn:0738204536 (p.129)
A `stable behaviour` which is also a `Liapunov stable behaviour`.
Synonyms: `stable behaviour` (urn:miriam:isbn:0738204536, p.129)
asymptotically stable behaviour
stable behaviour
urn:miriam:isbn:0738204536 (p.129)
A Behaviour is which is Liapunov Stable and not Attracting.
neutrally stable
urn:miriam:isbn:0738204536 (p.129)
1
2
saddle connection
A Temporal Behaviour connecting two Saddle Points.
urn:miriam:isbn:0738204536 (p.184)
1
homoclinic orbit
urn:miriam:isbn:0738204536 (p.161)
A Saddle Connection connecting a Saddle Point to itself.
Synonyms: Homoclinic Loop (urn:miriam:isbn:3540971416 p.213), Saddle Loop (http://www.egwald.ca/nonlineardynamics/mathappendix.php#limitset)
Homoclinic Loop
Saddle Loop
2
heteroclinic orbit
Heteroclinic Trajectory
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)).
A Saddle Connection connecting two different Saddle Points.
urn:miriam:isbn:0738204536 (p.166)
Synonyms: Heteroclinic Trajectory (urn:miriam:isbn:0738204536 p.166)
A `repelling` `asymptotic behaviour`.
Unstable Behaviour
repeller
A `limit behaviour` [TEDDY_0000085] with all behaviours starting sufficiently near to it will approach it as time goes to positive infinity.
DisplayName follows notation in urn:miriam:isbn:3817112823 (p.42).
attracting behaviour
stable behaviour
urn:miriam:isbn:0738204536 (p.128)
half-stable fixed point
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 Temporal Behaviour which is neither Attracting nor Unstable.
urn:miriam:isbn:0738204536 (p.129)
Non-Isolated Asymptotic Behaviour
A Cycle which is surrounded by other Cycles.
urn:miriam:isbn:0738204536 (p.196)
Neutrally Stable Cycle
non-isolated cycle
Obsolete: equivalent to TEDDY_0000083 'Temporal Behaviour'.
temporal behaviour ((obsolete))
A `behaviour` with respect to perturbations of the system or its environment.
perturbation behaviour
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 `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 `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
http://www.scholarpedia.org/article/Quasiperiodic_oscillations
quasiperiodic oscillating
urn:miriam:isbn:0738204536 (p.276)
stable fixed point
Sink
Attractor
urn:miriam:isbn:0738204536 (p.17)
A Fixed Point which is Stable.
stable limit cycle
A Limit Cycle which is Stable.
urn:miriam:isbn:0738204536 (p.196)
neutrally stable fixed point
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
synonym 'Infinite-Period Bifurcation': urn:miriam:isbn:0738204536 (p.262)
urn:miriam:isbn:0387983821 (p.59ff)
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
urn:miriam:isbn:0738204536 (p.253)
A `zero-eigenvalue bifurcation` in which a `stable fixed point` and an `unstable fixed point` coalesce and exchange their stability.
transcritical bifurcation
urn:miriam:isbn:0738204536 (p.50f)
A `zero-eigenvalue bifurcation` in which the fixed point is surrounded by two symmetrical fixed points on one side of the bifurcation.
pitchfork bifurcation
urn:miriam:isbn:0738204536 (p.55)
A `local bifurcation` in which one of the eigenvalue of the linarisation around the fixed point is zero at the bifurcation.
urn:miriam:isbn:0738204536 (p.248)
zero-eigenvalue bifurcation
A `pitchfork bifurcation` in which two symmetrical `unstable fixed points` collide with the stable fixed point and disappear.
subcritical pitchfork bifurcation
urn:miriam:isbn:0738204536 (p.58f)
A `pitchfork bifurcation` in which two symmetrical `stable fixed points` appear from the stable fixed point.
supercritical pitchfork bifurcation
urn:miriam:isbn:0738204536 (p.55f)
stable spiral point
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)
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
urn:miriam:isbn:0738204536 (p.196)
A Limit Cycle which is Unstable.
unstable fixed point
Repeller
urn:miriam:isbn:0738204536 (p.17)
Source
A Fixed Point which is Unstable.
inflexion point
amplitude
behaviour diversification
A `limit behaviour` [TEDDY_0000085] with all behaviours starting sufficiently near to it remain close to it.
liapunov stable behaviour
urn:miriam:isbn:0738204536 (p.129)
half-stable behaviour
urn:miriam:isbn:0738204536 (p.26,196)
An one-dimensional `fixed point` which is stable in one direction and unstable in the other direction or a two-dimensional `limit cycle` which is attracting outside and unstable inside or vice versa.
urn:miriam:isbn:0738204536 (p.20)
A `asymptotically stable behaviour` to which only behaviours starting in a restricted neighbourhood will converge.
only locally stable behaviour
A `asymptotically stable behaviour` to which all other behaviours will converge independent of the initial distance.
globally stable behaviour
urn:miriam:isbn:0738204536 (p.20)
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
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 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)
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 degenerated node
urn:miriam:isbn:0738204536 (p.137)
A Degenerated Node which is Stable, i.e. for which the Jacobian Matrix has two identical negative eigenvalues.
Stable Improper Node
urn:miriam:isbn:0738204536 (p.137)
unstable degenerated node
Unstable Improper Node
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 Temporal Behaviour which never repeats a state.
monotonicity
half-stable limit cycle
A Limit Cycle which is Half-Stable, i.e. the Limit Cycle is Attracting outside and Unstable inside or vice versa.
urn:miriam:isbn:0738204536 (p.196)
A `temporal behaviour` [TEDDY_0000083] which converges to some `limit behaviour` [TEDDY_0000085].
asymptotic behaviour
_obsolete