Modeling Nonlinear Dynamical Systems with Delay-differential Equations
Abstract
Description
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.
This paper is being submitted to the Journal of Nonlinear Sciences. This is a .tex file generated with SciWord 3.0. 17 pages. No figures. 01.03.17. Contact E-mail corrected, address added Contact address and e-mail updated
This paper is being submitted to the Journal of Nonlinear Sciences. This is a .tex file generated with SciWord 3.0. 17 pages. No figures. 01.03.17. Contact E-mail corrected, address added Contact address and e-mail updated