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Abstract and Applied Analysis
Volume 2014, Article ID 104156, 11 pages
http://dx.doi.org/10.1155/2014/104156
Research Article

Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks

1Department of Mathematics and Information Science, Zhoukou Normal University, Zhoukou, Henan 466001, China
2Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, China
3Institute of Information and System Computation Science, Beifang University of Nationalities, Yinchuan, Ningxia 750021, China

Received 10 March 2014; Accepted 19 May 2014; Published 4 June 2014

Academic Editor: Imran Naeem

Copyright © 2014 Huitao Zhao 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 delayed Lotka-Volterra predator-prey system with time delayed feedback is studied by using the theory of functional differential equation and Hassard’s method. By choosing appropriate control parameter, we investigate the existence of Hopf bifurcation. An explicit algorithm is given to determine the directions and stabilities of the bifurcating periodic solutions. We find that these control laws can be applied to control Hopf bifurcation and chaotic attractor. Finally, some numerical simulations are given to illustrate the effectiveness of the results found.