Mathematical Sciences: Nonlinear Strucured Growth Dynamics

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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.