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29 March 2024
 
  » arxiv » nlin.AO/0101038

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Modeling Nonlinear Dynamical Systems with Delay-differential Equations
Alexander N. Jourjine ;
Date 21 Dec 2000
Subject Adaptation and Self-Organizing Systems; Chaotic Dynamics | nlin.AO nlin.CD
AbstractWe describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial condition of a linear delay-differential system. It is further shown that the initial condition can be extended to a periodic solution of the delay-differential system if an appropriate choice of its parameters is made. As a result, any finite set of trajectories of a nonlinear dynamical system can be modeled with arbitrarily small error via a set of periodic solutions of a linear delay-differential equation. These results can be extended to some non-linear delay differential systems. One application of the method is for modeling memory and perception.
Source arXiv, nlin.AO/0101038
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