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




Stability and Bifurcation Analysis of a Delayed Leslie-Gower Predator-Prey System with Nonmonotonic Functional Response - Download this document for free, or read online. Document in PDF available to download.

Abstract and Applied AnalysisVolume 2013 2013, Article ID 152459, 19 pages

Research Article

Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China

Department of Mathematics, Tongji University, Shanghai 200092, China

Received 21 December 2012; Accepted 7 April 2013

Academic Editor: Kunquan Lan

Copyright © 2013 Jiao Jiang and Yongli Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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





Author: Jiao Jiang and Yongli Song

Source: https://www.hindawi.com/



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