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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 5649584, 21 pages
http://dx.doi.org/10.1155/2016/5649584
Research Article

Dynamical Analysis of a Computer Virus Model with Delays

1Department of Mathematics and Physics, Bengbu University, Bengbu 233030, China
2Laboratoire de Physique Statistique, Ecole Normale Supérieure, PSL Research University, Université Paris Diderot Sorbonne Paris-Cité, Sorbonne Universités, UPMC Univ Paris 06, CNRS, 24 rue Lhomond, 75005 Paris, France
3Department of Management, Polytechnic University of Marche, 60121 Ancona, Italy

Received 5 August 2016; Accepted 29 September 2016

Academic Editor: Vincenzo Scalzo

Copyright © 2016 Juan Liu 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

An SIQR computer virus model with two delays is investigated in the present paper. The linear stability conditions are obtained by using characteristic root method and the developed asymptotic analysis shows the onset of a Hopf bifurcation occurs when the delay parameter reaches a critical value. Moreover the direction of the Hopf bifurcation and stability of the bifurcating period solutions are investigated by using the normal form theory and the center manifold theorem. Finally, numerical investigations are carried out to show the feasibility of the theoretical results.