| Article ID: | iaor201110764 |
| Volume: | 218 |
| Issue: | 7 |
| Start Page Number: | 3733 |
| End Page Number: | 3745 |
| Publication Date: | Dec 2011 |
| Journal: | Applied Mathematics and Computation |
| Authors: | Tian Yanling, Weng Peixuan |
| Keywords: | game theory |
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.