The effect of diffusion for the multispecies Lotka-Volterra competition model

摘要

The purpose of this paper is to study the effect of diffusion in the existence of non-constant steady states for the Lotka-Volterra competition-diffusion system with three species, under Neumann boundary conditions. It will be shown that two large diffusion rates prevent the appearance of non-constant steady states, while if just one species diffuses fast non-constant equilibria may arise. The existence is shown by two methods, degree theory and bifurcation techniques. The stability of bifurcating steady states will be established. (C) 2003 Elsevier Science Ltd. All rights reserved. [References: 8]