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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 539684, 7 pages
http://dx.doi.org/10.1155/2014/539684
Research Article

Stability and Hopf Bifurcation Analysis on a Bazykin Model with Delay

1Department of Mathematics, School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China
2International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

Received 10 January 2014; Accepted 30 January 2014; Published 27 March 2014

Academic Editor: Hossein Jafari

Copyright © 2014 Jianming Zhang 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

The dynamics of a prey-predator system with a finite delay is investigated. We show that a sequence of Hopf bifurcations occurs at the positive equilibrium as the delay increases. By using the theory of normal form and center manifold, explicit expressions for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived.