Resident Invader Dynamics in Infinite Dimensional Systems


主講人:Professor Robert Stephen Cantrell,University of Miami




主講人介紹:1981年獲得猶他大學博士學位,導師為Klaus  Schmitt。自1982年先后歷經美國邁阿密大學數學系助理教授、副教授和教授,自2015年擔任數學系系主任。入選中國人民大學2015-2017年高層次外國專家。其主要研究領域為數學生態學、非線性分析和偏微分方程,在SIAM  Review、JDE、Trans AMS、Am Nat等權威學術期刊發表學術論文百余篇,并出版學術專著兩本。

內容介紹: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.