Resident Invader Dynamics in Infinite Dimensional Systems


主讲人:Professor Robert Stephen Cantrell,University of Miami




主讲人介绍:1981年获得犹他大学博士学位,导师为Klaus  Schmitt。自1982年先后历经美国迈阿密大学数学系助理教授、副教授和教授,自2015年担任数学系系主任。入选中国人民大学2015-2017年高层次外国专家。其主要研究领域为数学生态学、非线性分析和偏微分方程,在SIAM  Review、JDE、Trans AMS、Am Nat等权威学术期刊发表学术论文百余篇,并出版学术专著两本。

内容介绍: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.