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Zbl 1122.39005
Fazly, Mostafa; Hesaaraki, Mahmoud
Periodic solutions for a discrete time predator-prey system with monotone functional responses.
(English)
[J] C. R., Math., Acad. Sci. Paris 345, No. 4, 199-202 (2007). ISSN 1631-073X

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 $\Bbb R^{+}$, 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 2000:
*39A11 Stability of difference equations
39A12 Discrete version of topics in analysis
92D25 Population dynamics

Keywords: nonautonomous discrete time semi-ratio-dependent predator-prey system; Michaelis-Menten; Holling type-II and III; sigmoidal; Ivlev; monotone response functions

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