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On a periodic multi-species ecological model. (English) Zbl 1080.92059
Summary: A periodic predator-prey model with \(m\)-predators and \(n\)-preys is proposed, which can be seen as a modification of the traditional Lotka-Volterra model. By using a comparison theorem, the ultimately bounded region of the system is obtained. By using the comparison theorem and Brouwer fixed point theorem, sufficient conditions which guarantee the existence of positive periodic solutions of the system are obtained. Finally, by constructing a suitable Lyapunov function, some sufficient conditions are obtained for the existence of a unique globally attractive periodic solution of the system. The results obtained generalized the main results of J. D. Zhao and W. C. Chen in ibid. 147, No. 3, 881–892 (2004; Zbl 1029.92026).

MSC:
92D40 Ecology
34C25 Periodic solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
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