Journal
APPLIED MATHEMATICAL MODELLING
Volume 33, Issue 6, Pages 2748-2756Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2008.08.008
Keywords
Ratio-dependent predator-prey system; Positive periodic solution; Difference equation; Coincidence degree
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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. (C) 2008 Elsevier Inc. All rights reserved.
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