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

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January 2000, 6(1): 175-190. doi: 10.3934/dcds.2000.6.175

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

Yuan Lou ^1, , Salomé Martínez ^2, and Wei-Ming Ni ^2,

1.	Department of Mathematics, The Ohio State State University, Columbus, Ohio 43210
2.	School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, United States

Received October 1999 Published December 1999

Abstract
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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.

Keywords: degree theory, competition-diffusion systems, a priori estimates., Cross-diffusion.

Mathematics Subject Classification: 35J55, 92D2.

Citation: Yuan Lou, Salomé Martínez, Wei-Ming Ni. On $3\times 3$ Lotka-Volterra competition systems with cross-diffusion. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 175-190. doi: 10.3934/dcds.2000.6.175

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