Patterns of interacting populations in heterogeneous environments

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The goal of my research program is to mechanistically understand the effects of temporal and spatial variation on the dynamics of interacting populations and to study the patterns emerging from this interplay. The approach is to derive a variety of mathematical models and to study their behavior using analytical and numerical methods. The models are dynamical systems, given by ordinary or partial differential equations, difference or integrodifference equations, or some combination thereof. The techniques include linear and non-linear analysis, homogenization, stability theory, traveling waves, and numerical analysis. The program consists of several interconnected research directions, strategic and tactical, that inform and benefit from one another.