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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 245421, 10 pages
http://dx.doi.org/10.1155/2015/245421
Research Article

Multiple Bifurcations and Chaos in a Discrete Prey-Predator System with Generalized Holling III Functional Response

1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2Institute of Systems Biology, Shanghai University, Shanghai 200444, China
3School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China

Received 11 August 2014; Accepted 29 October 2014

Academic Editor: Mustafa Kulenović

Copyright © 2015 Xia Liu 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 prey-predator system with the strong Allee effect and generalized Holling type III functional response is presented and discretized. It is shown that the combined influences of Allee effect and step size have an important effect on the dynamics of the system. The existences of Flip and Neimark-Sacker bifurcations and strange attractors and chaotic bands are investigated by using the center manifold theorem and bifurcation theory and some numerical methods.