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

所提出的研究涉及奇摄动的单滞量的非线性时滞微分方程解。其目的是分析摄动参数小值时周期解的性态，并讨论在某些渐近长度为零的区间上出现的边界层现象。此外，还将从奇异摄动的角度研究某些可用有限差分方程组逼近的广义系统。这个项目是正在进行的了解非线性延迟-微分方程动力学的努力的一部分，该方程模拟了光学、生理学和种群生物学中的许多现象。

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.