Uniqueness of limit cycles in a harvested predator prey system with Holling type III functional response

Abstract

In this paper we considered a harvested predator-prey system with constant effort in which the predator response function is of the form Holling type-III. The dynamical behavior of the system near each of the equilibria is studied. Conditions for local asymptotic stability, persistence of the solutions, and isolated periodic solutions (limit cycles) are also derived. The uniqueness of limit cycles of this system is proved by using a lemma of Kooij and Zegeling (Nonlinear Analysis, TMA, 29, No. 6, 693-715, 1997). This proof also enables us to conclude that the local asymptotic stability of the system near the positive equilibrium implies its global asymptotic stability.