Abstract and Applied Analysis

Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays

Zizhen Zhang and Huizhong Yang

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 560804, 18 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449373

Digital Object Identifier
doi:10.1155/2013/560804

Mathematical Reviews number (MathSciNet)
MR3129336

Zentralblatt MATH identifier
1296.34169

Citation

Zhang, Zizhen; Yang, Huizhong. Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 560804, 18 pages. doi:10.1155/2013/560804. https://projecteuclid.org/euclid.aaa/1393449373


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