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Description

I'm interested in the spatiotemporal dynamics of predator-prey systems and what they imply about the makeup of ecological communities. In this talk, I'll describe some work which approaches this problem by formulating a relatively simple model of two interacting biological species situated in a habitat composed of two patches. The model consists of four coupled nonlinear ODE. I will present a fairly detailed bifurcation analysis intended to elucidate the origins of spatiotemporal patterns in the system. This amounts to a normal form analysis centered on the conjunction of two codimension-one bifurcations: a Hopf bifurcation and a bifurcation of Turing type. For reasonable values of the parameters, a higher-order degeneracy occurs as well. Thus, the resulting bifurcation is actually of codimension three. The outcome of all this will be a catalogue of all the dynamical behaviors which exist local to the bifurcation point.