  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.
