Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2015, Special Issue (2014), Article ID 620891, 12 pages.
Dynamic Analysis of a Delayed Reaction-Diffusion Predator-Prey System with Modified Holling-Tanner Functional Response
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.
Abstr. Appl. Anal., Volume 2015, Special Issue (2014), Article ID 620891, 12 pages.
First available in Project Euclid: 15 April 2015
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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