Propagation Phenomena for a Two-Species Lotka-Volterra Strong CompetitionSystem with Nonlocal Dispersal

Date:2019-10-18Clicks:10设置

Topic: Propagation Phenomena for a Two-Species Lotka-Volterra Strong CompetitionSystem with Nonlocal Dispersal

Speaker: Professor Zhao Xiaoqiang

Event date: 10/18/2019

Event time: 14:00 pm

Venue: Lecture Hall, Building 9

Sponsor: School of Mathematics and Statistics, Institute of Science and Technology

Abstract:

We consider the propagation phenomena for a two-species Lotka-Volterra strong competition system with nonlocal dispersal. We first establish the existence of bistable traveling waves by appealing to the theory of monotone semiflows. Then we use adynamical systems approach to prove that such a bistable traveling wave isasymptotically stable and unique modulo translation. Finally, we study the spreading properties of solutions for a class of initial conditions by the comparison arguments and the methods of super- and subsolutions. It is shown that for initial conditions where both species u and v are initially absent from the right half-line x > 0, and the species v dominates the species uaround x=-∞initially, if v spreads in absence of u slower than u in absence of v, then solutions of the initial value problem will approach a propagating terrace,which connects the unstable state (0,0) to the stable state (1, 0), and then the stable state (1,0) to the other stable state (0,1). This talk is based on ajoint work with Dr. Guo-Bao Zhang.


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