Necessary and sufficient conditions for the nonexistence of limit cycles of Leslie-Gower predator-prey models.

In this paper we consider a predator–prey model with Leslie–Gower functional response. We present the necessary and sufficient conditions for the nonexistence of limit cycles by the application of the generalized Dulac theorem. As a result, we give the necessary and sufficient conditions for which the local asymptotic stability of the positive equilibrium implies the global stability for this model. Our results extend and improve the results presented by Aghajani and Moradifam (2006) and Hsu and Huang (1995).