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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 $\Bbb R^{+}$, 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.

39A11Stability of difference equations (MSC2000)
39A12Discrete version of topics in analysis
92D25Population dynamics (general)
Full Text: DOI
[1] Bohner, M.; Fan, M.; Zhang, J.: Existence of periodic solutions in predator -- prey and competition dynamic systems. Nonlinear anal.: real world appl. 7, 1193-1204 (2006) · Zbl 1104.92057
[2] Fan, M.; Wang, Q.: Periodic solutions of a class of nonautonomous discrete time semi-ratio-dependent predator -- prey systems. Discrete contin. Dyn. syst. Ser. B 4, No. 3, 563-574 (2004) · Zbl 1100.92064
[3] Fazly, M.; Hesaaraki, M.: Periodic solutions for predator -- prey systems with beddington -- deangelis functional response on time scales. Nonlinear anal.: real world appl. (2007) · Zbl 1145.92035
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[6] Wang, Q.; Fan, M.; Wang, K.: Dynamics of a class of nonautonomous semi-ratio-dependent predator -- prey systems with functional responses. J. math. Anal. appl. 278, 443-471 (2003) · Zbl 1029.34042