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.

摘要努斯鲍姆这里提出的研究涉及两个领域：（a）具有状态相关时滞的非线性微分延迟方程的动力学和（b）关于保锥算子的问题。 (a) 和 (b) 之间的直接联系是最近发现的微分时滞方程的奇异极限与广义最大加方程之间的意外联系。 PI 将在多个方向继续开展这项工作。 例如，是否可以将已知结果扩展到两个或多个状态相关时滞的情况？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。许多物理问题最好通过函数微分方程来建模。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，科学模型传统上促使人们选择要研究的方程。尼科尔森五十年前的苍蝇种群模型就是一个典型的例子。 因此，该提案的更广泛影响是更好地理解涉及泛函微分方程的物理和生物科学模型。