On $3\times 3$ Lotka-Volterra competition systems with cross-diffusion

Abstract

In this paper we investigate the role of cross-diffusion in the $3\times 3$ Lotka-Volterra competition model. Of particular interest is the existence of non-constant steady states created by cross-diffusion in $3\times 3$ systems. A comparison with $2\times 2$ systems is also included.