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January  2006, 14(1): 135-148. doi: 10.3934/dcds.2006.14.135

Bifurcation structures of positive stationary solutions for a Lotka-Volterra competition model with diffusion II: Global structure

Yukio Kan-On 1,

1. 

Department of Mathematics, Faculty of Education, Ehime University, Matsuyama, 790-8577

Received  October 2004 Revised  February 2005 Published  October 2005

In this paper, we consider a Lotka-Volterra competition model with diffusion, and show that the global bifurcation structure of positive stationary solutions for the model is similar to that for a certain scalar reaction-diffusion equation. To do this, the comparison principle, the bifurcation theory, and the numerical verification are employed.
Keywords: Bifurcation structure, numerical verification., comparison principle.
Mathematics Subject Classification: 35B3.
Citation: Yukio Kan-On. Bifurcation structures of positive stationary solutions for a Lotka-Volterra competition model with diffusion II: Global structure. Discrete and Continuous Dynamical Systems, 2006, 14 (1) : 135-148. doi: 10.3934/dcds.2006.14.135
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