Qualitative analysis for a diffusive predator-prey model

Authors:
Bin Chen;Mingxin Wang
Affiliations:
Department of Mathematics, Yancheng Teachers College, Yancheng 224001, PR China and Department of Mathematics, Southeast University, Nanjing 210018, PR China;Department of Mathematics, Southeast University, Nanjing 210018, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 2
Cited 1

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SIAM Journal on Applied Mathematics
Qualitative behavior of solutions of chemotactic diffusion systems: effects of motility and chemotaxis and dynamics

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A strongly coupled predator-prey system with modified Holling-Tanner functional response

Computers & Mathematics with Applications

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Abstract

In this paper we study the qualitative properties of a diffusive predator-prey model subject to the homogeneous Neumann boundary condition. By a comparison argument and iteration technique, under some hypotheses we prove that the positive constant steady state is globally asymptotically stable. We also establish the existence and non-existence of non-constant positive steady states (stationary patterns) by use of the degree theory and the a priori estimates.