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

数学科学：奇异摄动微分时滞方程的边界层现象

• 批准号: 8713998
• 负责人: Roger Nussbaum
• 金额: $ 0.9万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-09-01 至 1989-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8713998&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Boundary; Layer; Phenomena

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.

本文研究了一类单时滞奇摄动非线性时滞微分方程。目的是分析扰动参数小值时周期解的行为，并讨论在渐近长度为零的一定区间上出现的边界层现象。此外，本文还从奇异摄动的角度研究了某些可以用有限差分方程近似的奇异系统。该项目是正在进行的努力的一部分，旨在理解非线性延迟微分方程的动力学，该方程模拟了光学，生理学和种群生物学中的许多现象。