Mathematical Sciences: Nonlinear Strucured Growth Dynamics

本研究的基本目标是开发和研究 结构种群动态的数学模型 为了探索和促进对 影响决定生长的生理特性， 个人的生育率和死亡率会对 人口水平的动态。 虽然有些模型， 出现在文献中将被研究和扩展， 重点将放在仔细推导模型， 结构化种群和多物种相互作用的类型 主要涉及大小和发育阶段（在某些情况下， 例实足年龄）的重要性和兴趣， 已附在生物学文献中， 以前被模仿过。 全系列标准以及 将采用最近开发的分析工具， 了解由此产生的模型动力学以及如何 它们取决于种群的内部结构， 模型参数，对非线性密度效应和性质 物种间的相互作用 需要模拟的问题是 选择的部分原因是有生物学研究可用于 与模型结果进行比较。 作为拟议的 研究，某些最近开发的分析方法将需要 以处理要使用的模型类型 本研究 并对模型的数值分析进行了展望 发挥重要作用。

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.