Permanence of the periodic predator-prey-mutualist system. (English) Zbl 1422.92135
Summary: In this paper, we study the permanence and the periodic solution of the periodic predator-prey-mutualist system. It is well known that mutualist species can reduce the capture rate of the predator species to the prey species. By further developing the analysis technique of Teng, a set of conditions which ensure the permanence of the system are obtained. In addition, sufficient conditions are derived for the existence of positive periodic solutions to the system. An example together with its numerical simulation shows the feasibility of the main results.
MSC:
| 92D25 | Population dynamics (general) |
| 34C25 | Periodic solutions to ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34D23 | Global stability of solutions to ordinary differential equations |
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