Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-03-20
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
A class of three-dimensional Gause-type predator-prey model is considered.
Firstly, local stability of equilibrium indicating the extinction of top-predator is obtained.
Meanwhile, we construct a Lyapunov function, which is an extension of the Lyapunov functions constructed by Hsu for predator-prey system (2005), to give the global stability of the equilibrium.
Secondly, we analyze the stability of coexisting equilibrium of predator-prey system with time delay when the predator catches the prey of pregnancy or with growth time.
The delay can lead to periodic solutions, which is consistent with the law of growth for birds and some mammals.
Further, an explicit formula is given which determines the stability of the bifurcating periodic solutions theoretically and the existence of periodic solutions is displayed by numerical simulations.
American Psychological Association (APA)
Guo, Shuang& Jiang, Weihua. 2012. Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-993088
Modern Language Association (MLA)
Guo, Shuang& Jiang, Weihua. Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System. Journal of Applied Mathematics No. 2012 (2012), pp.1-17.
https://search.emarefa.net/detail/BIM-993088
American Medical Association (AMA)
Guo, Shuang& Jiang, Weihua. Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-993088
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993088