Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 04, pp. 1-8.

Title: Global dynamics of a predator-prey model incorporating a constant prey refuge
        
Authors: Xiaolei Yu (Tianjin Univ. of Tech., Tianjin, China)
         Fuqin Sun  (Tianjin Univ. of Tech., Tianjin, China)
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 07, 2013.
Math Subject Classifications: 34D05, 34D20, 92D25.
Key Words: Predator-prey model; prey refuge; global stability.