Mathematical Sciences: Nonlinear Strucured Growth Dynamics

这项研究的基本目标是发展和研究结构化种群动态的数学模型，以便探索和促进理解决定个体生长、生育力和死亡率的生理特征对种群动态的影响。虽然文献中出现的一些模型将被研究和扩展，重点将是仔细推导某些类型的结构种群和多物种相互作用的模型，这些模型主要涉及大小和发育阶段（在某些情况下包括实足年龄），这在生物学文献中是很重要和感兴趣的，以前没有建模。为了了解由此产生的模型动力学以及它们如何依赖于种群的内部结构、关键模型参数、非线性密度效应和种间相互作用的性质，将应用一系列标准的和最近开发的分析工具。之所以选择要建立模型的问题，部分原因是已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，将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。预计模型的数值分析也将发挥重要作用。

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.