Hopf Bifurcation of an Improved SLBS Model under the Influence of Latent Period. (20th October 2013)

• Record Type: Journal Article
• Authors: Zhang, Chunming; Liu, Wanping; Xiao, Jing; Zhao, Yun
• Other Names: Mahomed Fazal M. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-10-20
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/196214
• Languages: English
• ISSNs: 1024-123X

Abstract

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.