Stability and Bifurcation Analysis of a Delayed Leslie-Gower Predator-Prey System with Nonmonotonic Functional Response
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-05-08
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Jiang, Jiao& Song, Yongli. 2013. Stability and Bifurcation Analysis of a Delayed Leslie-Gower Predator-Prey System with Nonmonotonic Functional Response. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-19.
https://search.emarefa.net/detail/BIM-449963
Modern Language Association (MLA)
Jiang, Jiao& Song, Yongli. Stability and Bifurcation Analysis of a Delayed Leslie-Gower Predator-Prey System with Nonmonotonic Functional Response. Abstract and Applied Analysis No. 2013 (2013), pp.1-19.
https://search.emarefa.net/detail/BIM-449963
American Medical Association (AMA)
Jiang, Jiao& Song, Yongli. Stability and Bifurcation Analysis of a Delayed Leslie-Gower Predator-Prey System with Nonmonotonic Functional Response. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-19.
https://search.emarefa.net/detail/BIM-449963
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-449963