Stable Patterns and Synchronization in Dynamical Systems

动态系统中的稳定模式和同步

• 批准号: 9704853
• 负责人: Jack Hale
• 金额: $ 12万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-09-01 至 2001-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704853&HistoricalAwards=false
• 关键词: Stable; Patterns; Synchronization; Dynamical; Systems

9704853 Hale The proposed research is concerned with the generation of stable patterns and synchronization in dynamical systems defined by ordinary differential equations on lattices, partial differential equations and delay differential equations. The primary interest is in the manner in which diffusive coupling, domain shape or boundary layer affect the dynamics and especially the stability of solutions. The mathematical tools involve singular perturbation theory, invariant manifolds and bifurcation. It is of paramount importance to understand the processor responsible for self organization, pattern formation and synchronization in various fields such as chemical kinetics, physics, biology, biochemistry and ecology. It has been known for some time that the nature of diffusive interaction of individual particles (or subsystems) plays a fundamental role. The main thrust of this project is to attempt to understand these phenomena and their dependence upon the coupling, domain shape and boundary conditions.

小行星9704853黑尔 所提出的研究关注的是稳定模式的生成 常微分方程定义的动力系统的同步 格上方程，偏微分方程和时滞微分 方程 主要的兴趣在于扩散的方式 耦合、畴形状或边界层影响动力学， 尤其是溶液的稳定性。 数学工具包括 奇异摄动理论，不变流形和分歧。 了解负责处理的处理器是至关重要的。 自组织、模式形成和各个领域的同步 如化学动力学、物理学、生物学、生物化学和生态学。 它 已经知道了一段时间，扩散相互作用的性质 单个粒子（或子系统）起着基本作用。 主要 这个项目的主旨是试图了解这些现象及其 依赖于耦合、域形状和边界条件。