ar X iv : n lin / 0 10 10 38 v 3 [ nl in . A O ] 1 N ov 2 00 1 Modeling Nonlinear Dynamical Systems with Delay - differential Equations

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finitetime 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.