Mathematical Sciences: Nonlinear Structured Growth Dynamics

拟议的研究涉及涉及结构种群的种群增长和多物种相互作用模型的研究，即个体生物的重要生长、死亡率和繁殖率显著依赖于诸如大小、年龄或发育阶段等生理特征的种群。在种群水平上，将探讨个体的这些生理特征对种群动态的影响。本文将对文献中出现的一些模型进行研究和推广。然而，重点将放在仔细推导某些类型的结构种群和多物种相互作用的新模型上，这些模型在生物学文献中受到重视和关注，以前没有建立模型。将应用一系列标准和最近开发的分析工具，在某些情况下，作为拟议研究的一部分，将扩展用于本研究。预计模型的数值分析也将发挥重要作用。

The proposed research is concerned with the study of models of population growth and multispecies interactions involving structured populations, i.e. populations for which the vital growth, mortality and fecundity rates of individual organisms are significantly dependent upon physiological traits such as size, age or developmental stage. The effects that such physiological traits of individuals have on the dynamics at the population level will be explored. Some models which have appeared in the literature will be studied and extended. The focus, however, will be on the careful derivation of new models for certain types of structured populations and multispecies interactions to which an importance and interest has been attached in the biological literature and which have not been previously modeled. A full range of standard as well as recently developed analytical tools will be applied and in some cases, as part of the proposed research, extended for use in this study. The numerical analysis of models is expected also to play an important role.