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Zbl 1080.92059
Chen, Fengde
On a periodic multi-species ecological model. (English)
[J] Appl. Math. Comput. 171, No. 1, 492-510 (2005). ISSN 0096-3003

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 {\it J. D. Zhao} and {\it W. C. Chen} in ibid. 147, No. 3, 881--892 (2004; Zbl 1029.92026).

MSC 2000:: *92D40 Ecology
34C25 Periodic solutions of ODE
34C60 Applications of qualitative theory of ODE
37N25 Dynamical systems in biology

Keywords: Prey-competition; Lyapunov function; Global asymptotic stability

Citations: Zbl 1029.92026

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