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

• Main Authors: Xiaolei Yu, Fuqin Sun
• Format: Article
• Language: English
• Published: Texas State University 2013-01-01
• Series: Electronic Journal of Differential Equations
• Subjects: Predator-prey model; prey refuge; global stability
• Online Access: http://ejde.math.txstate.edu/Volumes/2013/04/abstr.html

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.