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...

Full description

Saved in:
Bibliographic Details
Main Authors: Xinhong Pan, Min Zhao, Chuanjun Dai, Yapei Wang
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2015/620891
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1085-3375
1687-0409