Mathematical Sciences: Boundary Layer Phenomena for Singularly Perturbed Differential-Delay Equations

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The proposed research is concerned with singularly perturbed nonlinear delay-differential equations with one delay. The objective is to analyze the behavior of periodic solutions for small values of the perturbing parameter and to discuss the boundary layer phenomena that arise on certain intervals of asymptotic length zero. In addition, certain singular systems that can be approximated by finite-difference equations will be investigated from the point of view of singular perturbation. This project is part of ongoing efforts to understand the dynamics of nonlinear delay-differential equations that model many phenomena in optics, physiology and population biology.