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Modeling Nonlinear Dynamical Systems with Delay-differential Equations | Alexander N. Jourjine
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21 Dec 2000 | Subject: | Adaptation and Self-Organizing Systems; Chaotic Dynamics | nlin.AO nlin.CD | Abstract: | 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. | Source: | arXiv, nlin.AO/0101038 | Services: | Forum | Review | PDF | Favorites |
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