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.

AbstractNussBaumthe在这里提出的研究涉及两个领域：（a）具有状态依赖性时间滞后的非线性差分延迟方程的动力学（b）（b）有关呈锥锥的算子的问题。 （a）和（b）之间的直接联系是差异延迟方程与广义最大值方程之间的最近发现的意外连接。 PI将继续以多个方向继续这项工作。 例如，是否可以将已知结果扩展到两个或多个状态依赖的时间滞后？这在很大程度上是遗传的，但是数值结果表明了各种有趣的结果。理解非线性功能微分方程动态的一般问题在理论和实践中都很重要。许多物理问题最好由功能微分方程建模。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一些对模型的见解。 相反，科学中的模型传统上激发了研究方程式的选择。尼科尔森（Nicholson）五十年前的吹蝇种群模型是一个典型的例子。 因此，该提案的更广泛的影响是从涉及功能微分方程的物理和生物科学中更好地理解模型。