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

Jiao Jiang and Yongli Song

Abstract and Applied Analysis, 2013, vol. 2013, 1-19

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.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2013/152459.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2013/152459.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:152459

DOI: 10.1155/2013/152459

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().