Mathematical Sciences: Studies in Linear and Nonlinear Analysis

数学科学：线性和非线性分析研究

• 批准号: 9410557
• 负责人: Ying Huang
• 金额: $ 1.75万
• 依托单位: University of Toledo
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9410557&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Linear; Nonlinear

9410557 Huang It is proposed to continue the study of Floqoet theory for differential delay equations and dynamics of coupled oscillators. In pratice, a system often depends not only on its present states but also on past states. As a result, we are lead to the study of differential delay equations. Linear periodic systems constitute a very important in the field of differential delay equations. Studying Floquet theory of such systems enables one to understand the behavior and structure of their solutions. We plan to extend our study of Floquet theory for linear differential delay equations to broader classes of equations. We would also like to investigate the conditions under which there are no small solutions. Models of coupled osscillators arise naturally from problems in physics and biology. Since in pratice, oscillators can be coupled in many different ways,we can get a variety of equations that describe their motion. To understand the dynamics of these systems, we try to generalize the known results for two coupled oscillators to them. We also would like to study the stabilities of the discrete rotating waves and cluster solutions for globally coupled oscillators. ***

9410557黄建议继续研究微分时滞方程的流形理论和耦合振子的动力学。在实践中，一个系统往往不仅取决于它现在的状态，而且还取决于过去的状态。因此，我们引入了对时滞微分方程的研究。线性周期系统是时滞微分方程界中非常重要的一类。研究这类系统的Floquet理论使人们能够理解它们的解的行为和结构。我们计划将我们对线性时滞微分方程组的Floquet理论的研究扩展到更广泛的方程类。我们还想调查在哪些情况下没有小的解决办法。耦合振荡器的模型自然产生于物理学和生物学中的问题。因为在实际中，振子可以用许多不同的方式耦合，所以我们可以得到描述它们运动的各种方程。为了理解这些系统的动力学，我们尝试将两个耦合振子的已知结果推广到它们。我们还想研究全局耦合振子的离散旋转波解和簇解的稳定性。***