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群动态的数学模型，以探索和促进对确定个体生理特征的影响的理解，从而确定个体的生长，生育率和死亡率对人群水平的动态。 虽然将研究和扩展文献中出现的某些模型，但重点将放在某些类型的结构化种群和多物种相互作用的模型上，这些模型主要涉及大小和发育阶段（在某些情况下）（在某些情况下）对生物学文献中的重要性和兴趣及其重要性和兴趣所在，并且以前未被建模。 将应用一系列的标准以及最近开发的分析工具，以了解所得模型动力学以及它们如何依赖人群的内部结构，关键模型参数，非线性密度效应以及对间隙相互作用的性质。 部分选择要建模的问题是因为有生物学研究可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，以处理本研究中要使用的模型的类型。 预计模型的数值分析也将发挥重要作用。