Abstract
A four-compartment computer virus propagation model with two delays and graded infection rate is investigated in this paper. The critical values where a Hopf bifurcation occurs are obtained by analyzing the distribution of eigenvalues of the corresponding characteristic equation. In succession, direction and stability of the Hopf bifurcation when the two delays are not equal are determined by using normal form theory and center manifold theorem. Finally, some numerical simulations are also carried out to justify the obtained theoretical results.
Highlights
In recent years, with the fast development and popularization of computer technologies and network, Internet has offered numerous functionalities and facilities to the world
An improved model for propagation of computer virus propagation model in the network is introduced and studied by incorporating the delay due to the latent period of the computer viruses and the delay due to the period that the antivirus software needs to clean the viruses in the active computers into the model proposed in [19]
By choosing different combination of the two delays as a bifurcation parameter, it has been found that both the two delays can change the stability of the viral equilibrium of the model under some conditions
Summary
With the fast development and popularization of computer technologies and network, Internet has offered numerous functionalities and facilities to the world. All the computer virus models above which incorporate the latent status of the viruses assume that the latent computers have no infection ability This is not consistent with the reality, because an infected computer which is in latency can infect other computers through file copying or file downloading. The antivirus software needs a period to clean the viruses in the active computers. Based on this and motivated by the work about the dynamical system with delay in [20,21,22,23,24], we incorporate two delays into system (1) and obtain the following delayed computer virus model: μ−.
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