August  2006, 15(3): 725-746. doi: 10.3934/dcds.2006.15.725

Periodic solutions for a 3x 3 competitive system with cross-diffusion

1. 

Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile, silla 170 Correo 3, Santiago, Chile

2. 

School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Received  September 2005 Revised  January 2006 Published  April 2006

In this paper we study the role of cross-diffusion in the existence of spatially non-constant periodic solutions for the Lotka-Volterra competition system for three species. By properly choosing cross-diffusion coefficients, we show that Hopf bifurcation occurs at a constant steady state. Furthermore, these spatially nonhomogeneous periodic solutions are stable if diffusion rates are in appropriate ranges.
Citation: Salomé Martínez, Wei-Ming Ni. Periodic solutions for a 3x 3 competitive system with cross-diffusion. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 725-746. doi: 10.3934/dcds.2006.15.725
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