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Zbl 1217.34081
Guo, Haijun; Chen, Xiaoxing
Existence and global attractivity of positive periodic solution for a Volterra model with mutual interference and Beddington-DeAngelis functional response. (English)
[J] Appl. Math. Comput. 217, No. 12, 5830-5837 (2011). ISSN 0096-3003

The authors investigate a predator-prey model with positive p-periodic coefficients and with a Beddington-DeAngelis functional response. The aim is to prove the existence of a positive p-periodic, globally attractive solution. Defining appropriate operators in some Banach space, they use degree theory for Fredholm operators of index zero to show, under certain conditions, the existence and also the uniqueness of such a periodic solution. The authors thus obtain results that improve those of a recent paper by K. Wang and Y. L. Zhu.
[Josef Hainzl (Freiburg)]

MSC 2000:: *34C60 Applications of qualitative theory of ODE
92D25 Population dynamics
34C25 Periodic solutions of ODE
47N20 Appl. of operator theory to differential and integral equations
34D23 Global stability

Keywords: periodic predator-prey model; Beddington-DeAngelis functional response; positive periodic solution; global attractivity

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