Dynamics of Lotka-Volterra Competition Systems with Fokker-Planck Diffusion

Abstract

We consider competition systems of two species which have different dispersal strategies and interspecific competitive strengths. One of the dispersal strategies is random dispersal and the other is a Fokker-Planck diffusion whose motility is piecewise constant and jumps up when the resource is not enough. In this paper, first we show the Fokker-Planck diffusion allows ideal free distribution. Next we show the linear stability of semitrivial steady states is determined exactly by a threshold on the interspecific competitive strengths. Some conditions for coexistence and global asymptotic stability are also provided.