Asymptotic expansion for the solution of singularly perturbed delay differential equations

Singular perturbation problems occur in many areas, including biochemical kinetics, genetics, plasma physics, and mechanical and electrical systems. For practical problems, one seeks a uniformly valid, readily interpretable approximation to a solution that does not behave uniformly. In this paper we extend singular perturbation theory in ordinary differential equations to delay differential equations with a fixed lag. We aim to give an explicit sufficient condition so that the solution of a class of singularly perturbed delay differential equations can be asymptotically expanded. O'Malley-Hoppensteadt technique is adopted in the construction of approximate solutions for such problems. Some particular phenomena different from singularly perturbed ordinary differential equations are discovered.