Stability analysis of diffusive predator–prey model with modified Leslie–Gower and Holling-type III schemes

The stability of a diffusive predator–prey model with modified Leslie–Gower and Holling-type III schemes is investigated. A threshold property of the local stability is obtained for a boundary steady state, and sufficient conditions of local stability and un-stability for the positive steady state are also obtained. Furthermore, the global asymptotic stability of these two steady states are discussed. Our results reveal the dynamics of this model system.