Cone-Preserving Operators and Nonlinear Differential-Delay Equations

保锥算子和非线性微分时滞方程

• 批准号: 0401100
• 负责人: Roger Nussbaum
• 金额: --
• 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: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0401100&HistoricalAwards=false
• 关键词: Cone; Preserving; Operators; Nonlinear; Differential

AbstractNussbaumThe research proposed here concerns two areas: (a) the dynamics of nonlinear differential-delay equations with state-dependent time lag(s) and (b) questions about cone-preserving operators. The immediate link between (a) and (b) is a recently discovered and unexpected connection between singular limits of differential-delay equations and generalized max-plus equations. The PI will continue this work in several directions. For example, is it possible to extend known results to the case of two or more state-dependent time lags? This is largely terra incognita, but numerical results suggest a variety of intriguing results.The general problem of understanding the dynamics of nonlinear functional differential equations is important in both theory and practice. Many physical problems are best modeled by functional differential equations. Mathematical biology is a particularly rich source of examples. The methods developed here provide some insight into the models. Conversely, models in the sciences have traditionally motivated the choice of equations to study; Nicholson's model of blowfly population from fifty years ago is a typical example. Thus a broader impact of this proposal is obtaining a better understanding of models from the physical and biological sciences that involve functional differential equations.

本文主要研究两个方面的问题：(a)具有状态相关时滞的非线性微分时滞方程的动力学问题；(b)保锥算子问题。(a)和(b)之间的直接联系是最近在微分时滞方程的奇异极限和广义max-plus方程之间发现的意想不到的联系。PI将在几个方向上继续这项工作。例如，是否有可能将已知结果扩展到两个或多个状态相关的时间滞后的情况？这在很大程度上是未知领域，但数值结果表明了各种有趣的结果。理解非线性泛函微分方程动力学的一般问题在理论和实践中都很重要。许多物理问题最好用泛函微分方程来模拟。数学生物学是一个特别丰富的例子来源。这里开发的方法提供了对模型的一些见解。相反，传统上，科学中的模型推动了要研究的方程的选择；尼科尔森50年前的苍蝇种群模型就是一个典型的例子。因此，这一建议的一个更广泛的影响是，从涉及函数微分方程的物理和生物科学中获得对模型的更好理解。