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Existence of periodic solutions in a discrete predator-prey system with Beddington-DeAngelis functional responses. (English) Zbl 1237.39012

Summary: A discrete predator-prey model with Holling II and Beddington-DeAngelis functional responses is investigated. With the aid of differential equations with piecewise constant arguments, a discrete version of continuous nonautonomous delayed predator-prey model with Beddington-DeAngelis functional responses is proposed. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive solutions of the model are established.

MSC:

39A23 Periodic solutions of difference equations
39A12 Discrete version of topics in analysis
34A34 Nonlinear ordinary differential equations and systems
92D25 Population dynamics (general)
39A22 Growth, boundedness, comparison of solutions to difference equations
55M25 Degree, winding number
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