Modeling and Bifurcation Research of a Worm Propagation Dynamical System with Time Delay. (3rd July 2014)

• Record Type: Journal Article
• Authors: Yao, Yu; Zhang, Zhao; Xiang, Wenlong; Yang, Wei; Gao, Fuxiang
• Other Names: Zhao Yuxin Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2014(2014)
• Publication Date: 2014-07-03
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2014/408183
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Both vaccination and quarantine strategy are adopted to control the Internet worm propagation. By considering the interaction infection between computers and external removable devices, a worm propagation dynamical system with time delay under quarantine strategy is constructed based on anomaly intrusion detection system (IDS). By regarding the time delay caused by time window of anomaly IDS as the bifurcation parameter, local asymptotic stability at the positive equilibrium and local Hopf bifurcation are discussed. Through theoretical analysis, a threshold τ 0 is derived. When time delay is less than τ 0, the worm propagation is stable and easy to predict; otherwise, Hopf bifurcation occurs so that the system is out of control and the containment strategy does not work effectively. Numerical analysis and discrete-time simulation experiments are given to illustrate the correctness of theoretical analysis.