Mathematical Sciences: Nonlinear Strucured Growth Dynamics

数学科学：非线性结构增长动力学

• 批准号: 8714810
• 负责人: Jim Cushing
• 金额: $ 3.47万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-02-15 至 1989-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8714810&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Strucured; Growth

The fundamental goal of this research is to develop and study mathematical models for the dynamics of structured populations in order to explore and to contribute to the understanding of the effects that physiological traits which determine the growth, fertility and mortality rates of individuals can have on the dynamics at the population level. While some models which have appeared in the literature will be studied and extended, the focus will be on the careful derivation of models for certain types of structured populations and multispecies interactions involving primarily size and developmental stages (and in some cases chronological age) to which an importance and interest has been attached in the biological literature and which have not been previously modelled. A full range of standard as well as recently developed analytical tools will be applied in order to gain an understanding of the resulting model dynamics and how they depend on the internal structure of the populations, on key model parameters, on nonlinear density effects and on the nature of the interspecies interactions. Problems to be modelled were chosen in part because there are biological studies available for comparison to the model results. As part of the proposed research, certain recently developed analytical methods will need to be extended in order to handle the type of models to be used in this study. The numerical analysis of models is expected also to play an important role.

这项研究的基本目标是开发和研究结构化人口动态的数学模型，以探索并有助于理解决定个体生长、生育和死亡率的生理特征对人口的影响。人口层面的动态。 虽然文献中出现的一些模型将得到研究和扩展，但重点将放在仔细推导某些类型的结构化种群和多物种相互作用的模型上，主要涉及体型和发育阶段（在某些情况下按实际年龄），生物学文献已经给予了重视和兴趣，并且以前没有对其进行建模。 将应用全套标准以及最近开发的分析工具，以便了解所得到的模型动力学以及它们如何依赖于群体的内部结构、关键模型参数、非线性密度效应和种间相互作用的本质。 选择要建模的问题部分是因为有生物学研究可用于与模型结果进行比较。 作为拟议研究的一部分，需要扩展某些最近开发的分析方法，以便处理本研究中使用的模型类型。 模型的数值分析预计也将发挥重要作用。