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Permanence and stability of a two-predator-and-two competitive-prey system with Michaelis-Menten functional response. (Permanence and stability of a two-predator-and-two competitive-prey system with Machaelis-Menten functional response.) (Chinese. English summary) Zbl 1438.34151
Summary: In this article, a two-predator-and-two competitive-prey system with Michaelis-Menten functional response for the predator is investigated. Using the comparison theorem, the permanence of the system is obtained. Sufficient conditions for the global asymptotic stability of the system are presented through constructing a Liapunov function. Further, for the periodic case, a set of sufficient conditions is proved, which guarantee the existence, uniqueness and global asymptotic stability of a positive periodic solution. Numerical simulations illustrate the feasible of the main result.
MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D23 Global stability of solutions to ordinary differential equations
92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations
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