# American Institute of Mathematical Sciences

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

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

 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

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