Existence of positive periodic solution for ratio-dependent N-species difference system

In this paper, we propose a food web model consisting of n - 1 competing preys and one predator. Firstly, following the same idea and method in [M. Fan, K. Wang, Periodic solutions of discrete time nonautonomous ratio-dependent predator-prey system, Math. Comput. Model. 35 (2002) 951-961], we derive the discrete time analogue of the model. Then, the easily verifiable sufficient criteria are established for the existence of positive periodic solutions of this analogue, the approach is based on the coincidence degree and the related continuation theorem as well as some prior estimates. Meanwhile, some numerical simulations are carried out to support the theoretical analysis of the research.