Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 196214, 10 pages
http://dx.doi.org/10.1155/2013/196214
Research Article

Hopf Bifurcation of an Improved SLBS Model under the Influence of Latent Period

1School of Information Engineering, Guangdong Medical College, Dongguan 523808, China
2College of Computer Science, Chongqing University, Chongqing 400044, China

Received 12 June 2013; Accepted 15 August 2013

Academic Editor: Fazal M. Mahomed

Copyright © 2013 Chunming 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

A model applicable to describe the propagation of computer virus is developed and studied, along with the latent time incorporated. We regard time delay as a bifurcating parameter to study the dynamical behaviors including local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when the time delay passes through a sequence of critical values. A formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions is given by using the normal form method and center manifold theorem. Finally, illustrative examples are given to support the theoretical results.