American Institute of Mathematical Sciences

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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