Internet Worm Propagation Model With Time Delay And Its Bifurcation Analysis

With the development of the Internet, the worm propagation causes great damage for the Internet users. The worm propagation model is one of the important approach to research the worm propagation. Quarantine strategy is prominent in defending worms and has been applied to various worm propagation models. Although theoretical analysis suggests that worms must get eliminated under quarantine, such result does not appear in the real network. And there is a variety of reasons, the time delay considered in this paper which is aroused by the time window of intrusion detection system (IDS) exists in the propagation system is one of the main reasons.In this thesis, based on the research productions of epidemiology and nonlinear dynamics, the complex phenomena when the worm is propagating which is caused by the time delay of quarantine in the intrusion detection system is modeled and the time delay SIDQV model is proposed. After that, the numerical results of the SIDQV model are analyzed with using the real data of the Slammer worm and Code Red worm. Besides, the influence of the time delay in SIDQV model to the worm propagation is investigated and Hopf bifurcation in the worm propagation is also discussed.Some basic principles of Internet worm and bifurcation are introduced at the beginning of this thesis. Then, based on several classical worm propagation models, combining the time delay of quarantine in the intrusion detection system, the SIDQV model is proposed. By theoretical derivation, a delay critical value To of the SIDQV model is existence. When the time delay is less than τo, the worm propagation system is stable and easy to predict; when it is equal to or more than To, the Hopf bifurcation appears. Since it is easy to control and eliminate worms under a simple and stable worm propagation system without the Hopf bifurcation, the time window of IDS must be adjusted so that the time delay is less than τo, which ensures that the worm propagation system remains stable and worms can be eliminated thoroughly with certain containment strategy. At last, Matlab is selected to simulate the model, the critical value τo is verified by numerical results which is consistent with theoretical derivation.