Modeling Nonlinear Dynamical Systems with Delay-differential Equations

Details Modeling Nonlinear Dynamical Systems with Delay-differential Equations Modeling Nonlinear Dynamical Systems with Delay-differential Equations

2001-01-21

arxiv.org/abs/nlin/0101038v3

Nonlinear Sciences

Adaptation and Self-Organizing Systems

This paper is being submitted to the Journal of Nonlinear Sciences. This is a .tex file generated with SciWord 3.0. 17 pages.

Scientific paper

We 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.

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