Homoclinic Points for a Singularly Perturbed System of Differential Equations with Delay - Klevchuk, I. I. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
We obtain a representation of the integral manifold of a system of singularly perturbed differential-difference equations with periodic right-hand side. We show that, under certain conditions imposed on the right-hand side, the Poincaré map for the perturbed system has a transversal homoclinic point.