Abstract:

In 1974 Kaplan and Yorke introduced a new technique to relate a special class of delay differential equations to some ordinary differential systems. More precisely under convenient assumptions they studied the periodic solutions of the delay differential equation [dot x(t)=-f(x(t-1))-f(x(t-2)),] by studying the periodic solutions of an associated ordinary differential system.
Later on this method was developed widely, and many results have been established on the existence of periodic solutions of some delay differential equations. We will present a short summary of this method and of the delay differential equations where it can be applied.