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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 247269, 11 pages
http://dx.doi.org/10.1155/2015/247269
Research Article

Dynamic Behaviors of a Discrete Periodic Predator-Prey-Mutualist System

1College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350116, China
2Department of Mathematics, Ningde Normal University, Ningde, Fujian 352300, China

Received 3 June 2015; Accepted 1 September 2015

Academic Editor: Pavel Rehak

Copyright © 2015 Liya Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A nonautonomous discrete predator-prey-mutualist system is proposed and studied in this paper. Sufficient conditions which ensure the permanence and existence of a unique globally stable periodic solution are obtained. We also investigate the extinction property of the predator species; our results indicate that if the cooperative effect between the prey and mutualist species is large enough, then the predator species will be driven to extinction due to the lack of enough food. Two examples together with numerical simulations show the feasibility of the main results.