Abstract and Applied Analysis

Dynamic Analysis of a Delayed Reaction-Diffusion Predator-Prey System with Modified Holling-Tanner Functional Response

Xinhong Pan, Min Zhao, Chuanjun Dai, and Yapei Wang

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Abstract

A predator-prey model with modified Holling-Tanner functional response and time delays is considered. By regarding the delays as bifurcation parameters, the local and global asymptotic stability of the positive equilibrium are investigated. The system has been found to undergo a Hopf bifurcation at the positive equilibrium when the delays cross through a sequence of critical values. In addition, the direction of the Hopf bifurcation and the stability of bifurcated periodic solutions are also studied, and an explicit algorithm is obtained by applying normal form theory and the center manifold theorem. The main results are illustrated by numerical simulations.

Article information

Source
Abstr. Appl. Anal., Volume 2015, Special Issue (2014), Article ID 620891, 12 pages.

Dates
First available in Project Euclid: 15 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1429104599

Digital Object Identifier
doi:10.1155/2015/620891

Mathematical Reviews number (MathSciNet)
MR3326641

Zentralblatt MATH identifier
1344.92143

Citation

Pan, Xinhong; Zhao, Min; Dai, Chuanjun; Wang, Yapei. Dynamic Analysis of a Delayed Reaction-Diffusion Predator-Prey System with Modified Holling-Tanner Functional Response. Abstr. Appl. Anal. 2015, Special Issue (2014), Article ID 620891, 12 pages. doi:10.1155/2015/620891. https://projecteuclid.org/euclid.aaa/1429104599


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