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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

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