Abstract and Applied Analysis

Stability and Bifurcation Analysis of a Delayed Leslie-Gower Predator-Prey System with Nonmonotonic Functional Response

Jiao Jiang and Yongli Song

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Abstract

A delayed Leslie-Gower predator-prey model with nonmonotonic functional response is studied. The existence and local stability of the positive equilibrium of the system with or without delay are completely determined in the parameter plane. Using the method of upper and lower solutions and monotone iterative scheme, a sufficient condition independent of delay for the global stability of the positive equilibrium is obtained. Hopf bifurcations induced by the ratio of the intrinsic growth rates of the predator and prey and by delay, respectively, are found. Employing the normal form theory, the direction and stability of Hopf bifurcations can be explicitly determined by the parameters of the system. Some numerical simulations are given to support and extend our theoretical results. Two limit cycles enclosing an equilibrium, one limit cycle enclosing three equilibria and different types of heteroclinic orbits such as connecting two equilibria and connecting a limit cycle and an equilibrium are also found by using analytic and numerical methods.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 152459, 19 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511879

Digital Object Identifier
doi:10.1155/2013/152459

Mathematical Reviews number (MathSciNet)
MR3055860

Zentralblatt MATH identifier
1276.34073

Citation

Jiang, Jiao; Song, Yongli. Stability and Bifurcation Analysis of a Delayed Leslie-Gower Predator-Prey System with Nonmonotonic Functional Response. Abstr. Appl. Anal. 2013 (2013), Article ID 152459, 19 pages. doi:10.1155/2013/152459. https://projecteuclid.org/euclid.aaa/1393511879


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