Hopf Bifurcation of a Predator-Prey System with Delays and Stage Structure for the Prey
Joint Authors
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-28, 28 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-13
Country of Publication
Egypt
No. of Pages
28
Main Subjects
Abstract EN
This paper is concerned with a Holling type III predator-prey system with stage structure for the prey population and two time delays.
The main result is given in terms of local stability and bifurcation.
By choosing the time delay as a bifurcation parameter, sufficient conditions for the local stability of the positive equilibrium and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained.
In particular, explicit formulas that can determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form method and center manifold theorem.
Finally, numerical simulations supporting the theoretical analysis are also included.
American Psychological Association (APA)
Zhang, Zizhen& Yang, Huizhong. 2012. Hopf Bifurcation of a Predator-Prey System with Delays and Stage Structure for the Prey. Discrete Dynamics in Nature and Society،Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-460146
Modern Language Association (MLA)
Zhang, Zizhen& Yang, Huizhong. Hopf Bifurcation of a Predator-Prey System with Delays and Stage Structure for the Prey. Discrete Dynamics in Nature and Society No. 2012 (2012), pp.1-28.
https://search.emarefa.net/detail/BIM-460146
American Medical Association (AMA)
Zhang, Zizhen& Yang, Huizhong. Hopf Bifurcation of a Predator-Prey System with Delays and Stage Structure for the Prey. Discrete Dynamics in Nature and Society. 2012. Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-460146
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-460146