Study of a predator–prey model with modified Leslie–Gower and Holling type III schemes

A mathematical model of predator–prey system is studied analytically as well as numerically. The objective of this paper is to study systematically the dynamical properties of a modified Leslie–Gower predator–prey model with Holling type III functional response. We discuss different types of system behaviours for various parameter values. The essential mathematical features of the model with regard to the boundedness, stability and persistence have been carried out. Some numerical simulations are carried out to support our theoretical analysis. All the results are expected to be of use in the study of the dynamic complexity of ecosystem.