Boundary layer phenomena for differential-delay equations with state-dependent time lags: III

We consider a class of singularly perturbed delay-differential equations of the form where r=r(x(t)) is a state-dependent delay. We study the asymptotic shape, as ε→0, of slowly oscillating periodic solutions. In particular, we show that the limiting shape of such solutions can be explicitly described by the solution of a pair of so-called max-plus equations. We are able thereby to characterize both the regular parts of the solution graph and the internal transition layers arising from the singular perturbation structure.