Electron. J. Diff. Equ., Vol. 2013 (2013), No. 04, pp. 1-8.

Global dynamics of a predator-prey model incorporating a constant prey refuge

Xiaolei Yu, Fuqin Sun

Abstract:
In this article, a general predator-prey model incorporating a constant prey refuge with Hassell-Varley type functional response is studied. Sufficient conditions for the stability of the equilibria are obtained. It is shown that the positive equilibrium exists if predator death rate multiplied by a constants is smaller than its growth rate multiplied by capturing rate. Moreover, by constructing a Lyapunov function, it is shown that the positive equilibrium is globally stable.

Submitted May 8, 2012. Published January 7, 2013.
Math Subject Classifications: 34D05, 34D20, 92D25.
Key Words: Predator-prey model; prey refuge; global stability.

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Xiaolei Yu
School of Science
Tianjin University of Technology and Education
Tianjin 300222, China
email: 13752383154@126.com, yuxioalei12@126.com
Fuqin Sun
School of Science
Tianjin University of Technology and Education
Tianjin 300222, China
email: sfqwell@163.com

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