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.

所提出的研究涉及具有一延迟的奇异摄动非线性延迟微分方程。 目的是分析小扰动参数值的周期解的行为，并讨论渐近长度为零的某些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以用有限差分方程近似的奇异系统。 该项目是理解非线性时滞微分方程动力学的持续努力的一部分，该方程模拟了光学、生理学和群体生物学中的许多现象。