Open Access
2012 Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System
Shuang Guo, Weihua Jiang
J. Appl. Math. 2012: 1-17 (2012). DOI: 10.1155/2012/260798


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.


Download Citation

Shuang Guo. Weihua Jiang. "Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System." J. Appl. Math. 2012 1 - 17, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1248.34125
MathSciNet: MR2904519
Digital Object Identifier: 10.1155/2012/260798

Rights: Copyright © 2012 Hindawi

Vol.2012 • 2012
Back to Top