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Persistence and global stability in a delayed predator–prey system with Michaelis–Menten type functional response |
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| Authors: | Rui Xu M. A. J. Chaplain |
| Affiliation: | a Department of Mathematics, Mechanical Engineering College, 97 Heping West Road, Shijiazhuang 050003, People's Republic of China b Department of Mathematics, University of Dundee, Dundee DD1 4HN, UK |
| Abstract: | A delayed three-species predator–prey food-chain model with Michaelis–Menten type functional response is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive equilibrium of the system. |
| Keywords: | Delay Uniform persistence Stability Lyapunov functional |
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