Mathematical Sciences: Nonlinear Dynamical Systems

数学科学：非线性动力系统

• 批准号: 9014087
• 负责人: John Mallet-Paret
• 金额: $ 13.8万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-15 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9014087&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Dynamical; Systems

This project will study qualitative properties of nonlinear dynamical systems, with an emphasis on the following areas: (1) geometric theory of singularly perturbed differential equations, both finite and infinite dimensional; (2) differential delay equations arising in various areas (physiology, optics,biology) of science; and (3) dynamical systems exhibiting monotone and gradient-like behavior. In all these areas the focus will be on global structures such as attractors, periodic orbits, gradient structures and homo/heteroclinic orbits, and bifurcations of these structures.

该项目将研究非线性动力系统的定性特性，重点关注以下领域：（1）奇异摄动微分方程的几何理论，包括有限维和无限维； (2) 各个科学领域（生理学、光学、生物学）中出现的微分延迟方程； (3) 表现出单调和类梯度行为的动力系统。在所有这些领域中，重点将放在全局结构上，例如吸引子、周期轨道、梯度结构和同/异斜轨道，以及这些结构的分叉。