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

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 ofnon-constant steady states created by cross-diffusion in $3\times 3$ systems.A comparison with $2\times 2$ systems is also included.

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