Global Hopf Bifurcation on Two-Delays Leslie-Gower Predator-Prey System with a Prey Refuge
Joint Authors
Lin, Yiping
Cao, Jingnan
Liu, Qingsong
Source
Computational and Mathematical Methods in Medicine
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-06
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
A modified Leslie-Gower predator-prey system with two delays is investigated.
By choosing τ1 and τ2 as bifurcation parameters, we show that the Hopf bifurcations occur when time delay crosses some critical values.
Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions.
Numerical simulations are carried out to illustrate the theoretical results and chaotic behaviors are observed.
Finally, using a global Hopf bifurcation theorem for functional differential equations, we show the global existence of the periodic solutions.
American Psychological Association (APA)
Liu, Qingsong& Lin, Yiping& Cao, Jingnan. 2014. Global Hopf Bifurcation on Two-Delays Leslie-Gower Predator-Prey System with a Prey Refuge. Computational and Mathematical Methods in Medicine،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-485651
Modern Language Association (MLA)
Liu, Qingsong…[et al.]. Global Hopf Bifurcation on Two-Delays Leslie-Gower Predator-Prey System with a Prey Refuge. Computational and Mathematical Methods in Medicine No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-485651
American Medical Association (AMA)
Liu, Qingsong& Lin, Yiping& Cao, Jingnan. Global Hopf Bifurcation on Two-Delays Leslie-Gower Predator-Prey System with a Prey Refuge. Computational and Mathematical Methods in Medicine. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-485651
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-485651