TY - JOUR
T1 - Hopf Bifurcation of a Nonresident Computer Virus Model with Delay
JO - Analysis in Theory and Applications
VL - 3
SP - 199
EP - 208
PY - 2018
DA - 2018/11
SN - 34
DO - http://doi.org/10.4208/ata.OA-2016-0035
UR - https://global-sci.org/intro/article_detail/ata/12835.html
KW - Computer virus, delay, Hopf bifurcation, SLA model, Periodic solution.
AB - <p style="text-align: justify;">In this paper, a delayed nonresident computer virus model with graded infection
rate is considered in which the following assumption is imposed: latent computers
have lower infection ability than infectious computers. With the aid of the bifurcation
theory, sufficient conditions for stability of the infected equilibrium of the model
and existence of the Hopf bifurcation are established. In particular, explicit formulae
which determine direction and stability of the Hopf bifurcation are derived by means
of the normal form theory and the center manifold reduction for functional differential
equations. Finally, a numerical example is given in order to show the feasibility of the
obtained theoretical findings.</p>