# American Institute of Mathematical Sciences

July  2009, 23(3): 1061-1072. doi: 10.3934/dcds.2009.23.1061

## Qualitative analysis of a diffusive variable-territory prey-predator model

 1 Department of Mathematics, Southeast University, Nanjing 210018, and School of Math. Science, Xuzhou Normal University, Xuzhou 221116, China 2 Department of Mathematics, National University of Singapore, 2 Science Drive 2, Republic of Singapore 117543, Singapore

Received  March 2008 Revised  September 2008 Published  November 2008

In this paper, we study the variable-territory prey-predator model. We first establish the global stability of the unique positive constant steady state for the ODE system and the reaction diffusion system, and then prove the existence, uniqueness and stability of positive stationary solutions for the heterogeneous environment case.
Citation: Mingxin Wang, Peter Y. H. Pang. Qualitative analysis of a diffusive variable-territory prey-predator model. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 1061-1072. doi: 10.3934/dcds.2009.23.1061
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