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August  2004, 4(3): 653-662. doi: 10.3934/dcdsb.2004.4.653

Persistence and periodic solutions of a nonautonomous predator-prey diffusion with Holling III functional response and continuous delay

Zhijun Liu 1, and  Weidong Wang 1,

1. 

Department of Mathematics, Hubei Institute for Nationalities, Enshi 445000, China, China

Received  September 2002 Revised  December 2003 Published  May 2004

A nonautonomous diffusion model with Holling III functional response and continuous time delay is considered in this paper, where all parameters are time dependent and the prey can diffuse between two patches of a heterogeneous environment with barriers between patches, but for the predator the diffusion does not involve a barrier between patches. It is shown that the system is persistent under any diffusion rate effect. Moreover, sufficient conditions that guarantee the existence of a positive periodic solution which is globally asymptotic stable are obtained.
Keywords: persistence, Holling III functional response, global attractivity., diffusion, Prey–predator system, continuous time delay.
Mathematics Subject Classification: Primary: 92C15, 34C2.
Citation: Zhijun Liu, Weidong Wang. Persistence and periodic solutions of a nonautonomous predator-prey diffusion with Holling III functional response and continuous delay. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 653-662. doi: 10.3934/dcdsb.2004.4.653
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