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Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system. (English) Zbl 1050.39022
Summary: With the help of differential equations with piecewise constant arguments, we first propose a discrete analogue of continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modeling the dynamics of the prey and the predator having nonoverlapping generations. Then, easily verifiable sufficient criteria are established for the existence of positive periodic solutions. The approach is based on the coincidence degree and the related continuation theorem as well as some a priori estimates.

MSC:
39A12Discrete version of topics in analysis
39A11Stability of difference equations (MSC2000)
92D25Population dynamics (general)