Periodic solutions for predator-prey systems with Beddington-DeAngelis functional response on time scales. (English) Zbl 1145.92035

Summary: This paper deals with the question of existence of periodic solutions of nonautonomous predator-prey dynamical systems with Beddington-DeAngelis functional response. We explore the periodicity of this system on time scales. New sufficient conditions are derived for the existence of periodic solutions. These conditions extend previous results presented by M. Bohner, M. Fan and J. Zhang [Existence of periodic solutions in predator-prey and competition dynamic systems. Nonlinear. Anal. Real World Appl. 7, No. 5, 1193–1204 (2006; Zbl 1104.92057)]; M. Fan and Y. Kuang [Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelies functional response. J. Math. Anal. Appl. 295, No. 1, 15–39 (2004; Zbl 1051.34033)] and J. Zhang and J. Wang [Periodic solutions for discrete predator-prey systems with the Beddington-DeAngelis functional response. Appl. Math. Lett. 19, No. 12, 1361-1366 (2006; Zbl 1140.92325)].


92D40 Ecology
39A11 Stability of difference equations (MSC2000)
37N25 Dynamical systems in biology
39A12 Discrete version of topics in analysis
Full Text: DOI


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