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Ding, Xiaoquan; Zhao, Gaifang

Periodic solutions for a semi-ratio-dependent predator-prey system with delays on time scales. (English) Zbl 1248.34140

Discrete Dyn. Nat. Soc. 2012, Article ID 928704, 15 p. (2012).
Summary: This paper is devoted to the existence of periodic solutions for a semi-ratio-dependent predator-prey system with time delays on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic solutions. Our results show that for the most monotonic prey growth such as the logistic, the Gilpin, and the Smith growth, and the most celebrated functional responses such as the Holling type, the sigmoidal type, the Ivlev type, the Monod-Haldane type, and the Beddington-DeAngelis type, the system always has at least one periodic solution. Some known results are shown to be special cases of the present paper.

Cited in 4 Documents

MSC:

34N05 Dynamic equations on time scales or measure chains
92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations

Keywords:

semi-ratio-dependent predator-prey system; time delays on time scales
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References:

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