Dynamics of Functional Differential Equations with Applications to Biology and Ecology

泛函微分方程动力学及其在生物学和生态学中的应用

• 批准号: RGPIN-2015-05686
• 负责人: Wang, Lin
• 金额: $ 1.24万
• 依托单位: University of New Brunswick
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635684
• 关键词: Dynamics; Functional; Differential; Equations; Applications

Many biological and ecological processes involve time lags. For example, a predator needs time to convert its consumption of prey to its biomass; for many infectious diseases, time lags exist due to dispersal of populations and disease state changes. To model these time-lag involving processes, a natural choice is to use functional differential equations (i.e., differential equations subject to delays). In contrast to systems described by ordinary differential equations, the initial state of a functional differential equation is a function specified on an interval and the associated phase space is infinite dimensional. Since the resulting dynamical systems are infinite dimensional, the analysis of functional differential equations is extremely challenging, especially for equations with delay-dependent coefficients, nonlinearity and multiple state variables, which happen to be typical features of equations risen from biology and ecology.

许多生物学和生态过程都涉及时间滞后。例如，捕食者需要时间将其猎物消耗转换为生物量。对于许多传染病，由于种群的分散和疾病状态的变化，时间滞后存在。为了对这些涉及过程的时间段进行建模，一种自然的选择是使用功能微分方程（即，差异方程式可能会延迟）。与普通微分方程描述的系统相反，功能微分方程的初始状态是在间隔上指定的函数，相关的相空间是无限的尺寸。由于所得的动力学系统是无限的维度，因此功能微分方程的分析极具挑战性，尤其是对于具有延迟依赖性系数，非线性和多个状态变量的方程式，这恰好是从生物学和生态学方程式中的典型特征。