Existence and uniqueness of globally attractive positive almost periodic solution in a predator-prey dynamic system with Beddington-DeAngelis functional response. (English) Zbl 1472.34100

Wu, Wenquan

Abstr. Appl. Anal. 2014, Article ID 204564, 9 p. (2014).

Summary: This paper is concerned with a predator-prey system with Beddington-DeAngelis functional response on time scales. By using the theory of exponential dichotomy on time scales and fixed point theory based on monotone operator, some simple conditions are obtained for the existence of at least one positive (almost) periodic solution of the above system. Further, by means of Lyapunov functional, the global attractivity of the almost periodic solution for the above continuous system is also investigated. The main results in this paper extend, complement, and improve the previously known result. And some examples are given to illustrate the feasibility and effectiveness of the main results.

MSC:

34C60	Qualitative investigation and simulation of ordinary differential equation models
92D25	Population dynamics (general)
34N05	Dynamic equations on time scales or measure chains
34C27	Almost and pseudo-almost periodic solutions to ordinary differential equations
34D20	Stability of solutions to ordinary differential equations
34D09	Dichotomy, trichotomy of solutions to ordinary differential equations
47N20	Applications of operator theory to differential and integral equations

Keywords:

predator-prey system; exponential dichotomy; fixed point theory; positive (almost) periodic solution; global attractivity

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