Colloquium | Institute of Mathematical Sciences
Time：15:30-16:30, May 17, Friday (16:30-17:00 Refreshment)
Location：IMS, S407
Speaker: Robert Stephen Cantrell, Renmin University of China and University of Miami
Abstract: Motivated by evolutionary biology, we study general infinite-dimensional dynamical systems involving two species - a resident and an invader- that are identical except for their strategies relative to a particular trait (e.g., their rate of advective movement up a resource gradient). Sufficient conditions for competitive exclusion phenomena are given when the two species play similar strategies. Those conditions are based on invasibility criteria, for instance, evolutionarily stable strategies in the framework of adaptive dynamics. Such questions were first proposed and studied by Stefan Geritz and collaborators for a class of ordinary differential equations. We extend and generalize previous work in two directions. First, we consider analytic semiflows in infinite-dimensional spaces. Secondly, we devise an argument based on Hadamard’s Graph Transform methods that does not depend on the monotonicity of the two-species system. Our results are applicable to a wide class of reaction-diffusion models as well as models with nonlocal diffusion operators.