dynamical system

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dynamical system

n.
Mathematics A space together with a transformation of that space, such as the solar system transforming over time according to the equations of celestial mechanics.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.dynamical system - (physics) a phase space together with a transformation of that space
phase space - (physics) an ideal space in which the coordinate dimensions represent the variables that are required to describe a system or substance; "a multidimensional phase space"
natural philosophy, physics - the science of matter and energy and their interactions; "his favorite subject was physics"
chaos - (physics) a dynamical system that is extremely sensitive to its initial conditions
References in periodicals archive ?
For a more exhaustive qualitative analysis of a nonlinear dynamic system, it is compulsory to identify both singularities of the parameter plane and singularities of the phase plane [31].
Generally, behaviors of a nonlinear dynamic system may change with varying parameters; a stable equilibrium can become unstable and a periodic oscillation may occur or a new equilibrium may appear making the previous equilibrium unstable once the parameters vary.
Then function V(v(t)) = [v.sup.T] (t)Pv(t) is a Lyapunov one for the nonlinear dynamic system (17).
Cellular neural networks can produce a kind of chaos phenomenon which is a complex nonlinear dynamic system and is similar to random process of nonlinear systems with certainties.
In order to solve the [H.sub.[infinity]] quasi-sliding mode controller gain K in the switching surface and optimized performance of noise perturbation attenuation [gamma] > 0, we use the LMI formulation to look for them such that the nonlinear dynamic system (1) is asymptotically stable in the quasi-sliding mode.
Circuits of nonlinear dynamic system provide an excellent tool for the study of chaotic behavior.
The chaos synchronization phenomenon has the following feature: the trajectories of the master and the slave chaotic system are identical in spite of starting from different initial conditions or different nonlinear dynamic system. However, slight differentiations of initial conditions, for chaotic dynamical systems, will lead to completely different trajectories [1-14].
Since neural network has the capability to approximate any nonlinear function, the tracking control using neural network for nonlinear dynamic system has become a promising research topic.
The problem addressed is the steady-state optimization of a nonlinear dynamic system as stated below:
This fascinating paper discusses an experiment that drew on a nonlinear dynamic system simulation and precepts derived from personality trait theory.
Lee, "Partial tracking error constrained fuzzy dynamic surface control for a strict feedback nonlinear dynamic system," IEEE Transactions on Fuzzy Systems, vol.
T-S fuzzy model is sensitive to the numbers of nonlinear terms--the numbers of fuzzy rules are generated according to the numbers of nonlinear terms in a nonlinear dynamic system. Therefore, if there are lots of nonlinear terms in a dynamic system, the modeling process should be complicated and numerous modeling materials are required.

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