Abstract and Applied Analysis

Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays

Huitao Zhao, Yiping Lin, and Yunxian Dai

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Abstract

A ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998) for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 321930, 15 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449714

Digital Object Identifier
doi:10.1155/2013/321930

Mathematical Reviews number (MathSciNet)
MR3147782

Zentralblatt MATH identifier
1295.34091

Citation

Zhao, Huitao; Lin, Yiping; Dai, Yunxian. Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 321930, 15 pages. doi:10.1155/2013/321930. https://projecteuclid.org/euclid.aaa/1393449714


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