Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system

Authors:
Meng Fan;Ke Wang
Affiliations:
Department of Mathematics, Northeast Normal University 138 Renmin Street, Changchun, Jilin, 130024, P.R. China;Department of Mathematics, Northeast Normal University 138 Renmin Street, Changchun, Jilin, 130024, P.R. China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2002

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Abstract

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 priori estimates.