Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2012, Special Issue (2012), Article ID 841987, 16 pages.
Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus
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.
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 841987, 16 pages.
First available in Project Euclid: 1 April 2013
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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