Abstract and Applied Analysis

Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus

Tao Dong, Xiaofeng Liao, and Huaqing Li

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Abstract

By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti-virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes through a sequence of critical value. The linerized model and stability of the bifurcating periodic solutions are also derived by applying the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 841987, 16 pages.

Dates
First available in Project Euclid: 1 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364845132

Digital Object Identifier
doi:10.1155/2012/841987

Mathematical Reviews number (MathSciNet)
MR2910735

Zentralblatt MATH identifier
1237.37067

Citation

Dong, Tao; Liao, Xiaofeng; Li, Huaqing. Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 841987, 16 pages. doi:10.1155/2012/841987. https://projecteuclid.org/euclid.aaa/1364845132


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