# American Institute of Mathematical Sciences

September  2007, 8(2): 435-454. doi: 10.3934/dcdsb.2007.8.435

## A competition-diffusion system with a refuge

 1 Department of Mathematics, University of Science and Technology of China, Hefei 230026, China, China

Received  October 2006 Revised  March 2007 Published  June 2007

In this paper, a model composed of two Lotka-Volterra patches is considered. The system consists of two competing species $X, Y$ and only species $Y$ can diffuse between patches. It is proved that the system has at most two positive equilibria and then that permanence implies global stability. Furthermore, to answer the question whether the refuge is effective to protect $Y$, the properties of positive equilibria and the dynamics of the system are studied when $X$ is a much stronger competitor.
Citation: Daozhou Gao, Xing Liang. A competition-diffusion system with a refuge. Discrete and Continuous Dynamical Systems - B, 2007, 8 (2) : 435-454. doi: 10.3934/dcdsb.2007.8.435
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