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

Yukio Kan-On

doi:10.3934/dcds.2006.14.135

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2006, Volume 14, Issue 1: 135-148. Doi: 10.3934/dcds.2006.14.135

This issue Previous Article An introduction to joinings in ergodic theory Next Article Some aspects of recent works on limit theorems in ergodic theory with special emphasis on the "central limit theorem''

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: September 30, 2004

Revised: January 31, 2005

Published: February 2006

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Abstract

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.

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Mathematics Subject Classification: 35B32.

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