ASYMPTOTIC SOLUTION FOR A SYSTEM OF SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS^∗

This paper is mainly aimed to investigate the asymptotic solution for a system of singularly perturbed delay differential equations. In order to establish the step–like asymptotic solution, the basic framework of contrast structure theory is employed. Some sufficient criteria for the existence of asymptotic solution will be proposed. After that, by means of the boundary layer functions method and sewing method, the expansion for the asymptotic solution will be constructed and the existence of a uniformly valid continuous solution is proved. Finally, the effectiveness of the established results is validated via a concrete example.