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Periodic solutions for a discrete time predator-prey system with monotone functional responses. (English) Zbl 1122.39005
Summary: Sharp sufficient conditions for the existence of periodic solutions of a nonautonomous discrete time semi-ratio-dependent predator-prey system with functional responses are derived. In our results this system with any monotone functional response bounded by polynomials in \(\mathbb R^{+}\), always has at least one \(\omega\)-periodic solution. In particular, this system with the most popular functional responses Michaelis-Menten, Holling type-II and III, sigmoidal, Ivlev and some other monotone response functions, always has at least one \(\omega\)-periodic solution.

MSC:
39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
92D25 Population dynamics (general)
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