Application of Asymptotic Methods to Regularly and Singularly Perturbed Differential-Difference Equations

Abstract

We consider a singularly perturbed system of differential-difference equations and obtain a representation of the integral manifold of this system. The averaging method is applied to the investigation of periodic solutions of a conservative system with small delay. We apply the second approximation of the averaging method to the analysis of stability of a system of weakly coupled oscillators with time delay. A sufficient stability (instability) condition is established for a linear system of differential-difference equations.