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

Mingxin Wang; Peter Y. H. Pang

doi:10.3934/dcds.2009.23.1061

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2009, Volume 23, Issue 3: 1061-1072. Doi: 10.3934/dcds.2009.23.1061

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

Mingxin Wang^1, and
Peter Y. H. Pang^2,

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

Received: February 29, 2008

Revised: August 31, 2008

Published: August 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J55; Secondary: 92D25.

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