Modeling and Bifurcation Research of a Worm Propagation Dynamical System with Time Delay

作者：Yao Yu^*; Zhang Zhao; Xiang Wenlong; Yang Wei; Gao Fuxiang

来源：Mathematical Problems in Engineering, 2014, 2014: 408183.

DOI：10.1155/2014/408183

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 tau(0) is derived. When time delay is less than tau(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.

• 出版日期2014
• 单位东北大学