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 ?
It is possible to obtain a discrete dynamical system from a continuous dynamical system through the sampling of its solution at a regular time interval T, in which the dynamical rule representing the relationship between the consecutive sampled values of the dynamical variables is regarded as a time T map.
Given dynamical system f : S [right arrow] S, S [subset] R, the iterations of the function f are the composition of a function with itself.
This special issue places its emphasis on the study of the applications of dynamical system on time scales; such applications include economics models utilizing optimal control theory, fractional calculus, and the development of new population models.
Reconstructed image pixels were obtained by using the initial value problem of differential equations describing the dynamical system, for example, a continuous-time image reconstruction (CIR) system.
When the states of the entities are updated in a synchronous manner, the system is called a parallel dynamical system (PDS) [2, 3], while if they are updated in an asynchronous way, the system is named sequential dynamical system (SDS) [4].
Consider the following three-dimensional dynamical system:
On the dynamical system (X , a; w), one has [M.sub.[sigma]] (w) = [M.sub.[tau]].
where [OMEGA] is a metric space, E is a finite-dimensional Banach space, ([OMEGA], [Z.sub.+], [sigma]) is a dynamical system with discrete time [Z.sub.+], [E] is the space of all the linear operators acting on E equipped with operator norm, C([OMEGA], [E]) (respectively, C(E x [OMEGA], E)) is the space of all the continuous functions defined on [OMEGA] (respectively, on E x [OMEGA]) with values in [E] (respectively, E) equipped with compact-open topology and F is a "small" perturbation.
These chapters include discussions of such important issues as the long-run survival of weakly, strictly, and iteratively strictly dominated strategies, and the mapping between stationary states of the dynamical system on the one hand, and aggregate Nash equilibrium behavior (the static solution concepts discussed in Chapter One) and evolutionary stability criteria (the quasidynamic solution concepts discussed in Chapter Two) on the other.
The simplest chaotic dynamical system is the Bernoulli shift described by Palmore [8]:

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