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Abstract and Applied Analysis
Volume 2013, Article ID 560804, 18 pages
http://dx.doi.org/10.1155/2013/560804
Research Article

Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays

1Key Laboratory of Advanced Process Control for Light Industry, Jiangnan University, Wuxi 214122, China
2School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China

Received 18 August 2013; Accepted 26 August 2013

Academic Editor: Luca Guerrini

Copyright © 2013 Zizhen Zhang and Huizhong Yang. 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

This paper is concerned with a computer virus model with two delays. Its dynamics are studied in terms of local stability and Hopf bifurcation. Sufficient conditions for local stability of the positive equilibrium and existence of the local Hopf bifurcation are obtained by regarding the possible combinations of the two delays as a bifurcation parameter. Furthermore, explicit formulae for determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are obtained by using the normal form method and center manifold theory. Finally, some numerical simulations are presented to support the theoretical results.