COMPLEX DYNAMICS IN A DELAY PREDATOR-PREY MODEL WITH SELECTIVE RECRUITMENT AND MIXED FUNCTIONAL RESPONSE

Rongping Zhu (P. R. China) and Hong Zhang (P. R. China)

Received September 4, 2007; Revised February 23, 2008

Abstract

In this paper, we study a predator-prey model with selective recruitment which incorporates a delay term and mixed functional response. The local stability of the trivial equilibria is analyzed and it is found out that the set of such equilibria consists of a unstable node and two saddle points. It is also noted that the positive equilibrium is locally asymptotically stable when time delay is suitable small, while a loss of stability by a Hopf bifurcation can occur as time delay increase. Some sufficient conditions which guarantee the uniform persistence of the model and the global stability of the positive equilibrium are also given. In this respect, it is seen that the delay has no effect upon the persistence of the model. Finally, a numerical simulation is provided and some concluding remarks are given.

Keywords and phrases: predator-prey model, equilibrium, Hopf bifurcation, uniform persistence, global stability.