Resident-Invader Dynamics in Infinite Dimensional Systems

发布时间：2018-06-25 作者：浏览次数：

Speaker:	Stephen Cantrell	DateTime:	2018年6月26日（周二）上午9:30-10:30
Brief Introduction to Speaker: Stephen Cantrell，University of Miami.		Place:	六号楼二楼报告厅
Abstract:Motivated by evolutionary biology, we study general infinite-dimensional dynamical systems involving two species - the resident and the invader. Sufficient conditions for competition exclusion phenomena are given when the two species plays similar strategies. Those conditions are based on invasibility criteria, for instance, evolutionarily stable strategies in the framework of adaptive dynamics. This type of question was first proposed and studied for a class of ordinary differential equations in (S. Geritz et al., J. Math. Biol., 2002) and (S. Geritz,J. Math. Biol. 2005). We extend and generalize previous works in two directions. First, we consider analytic semiflows in infinite-dimensional spaces. Secondly, we device an argument based on Hadamard’s graph transform method 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.