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

Yu Yao,Wenlong Xiang,Fuxiang Gao,Wei Yang,Zhao Zhang

doi:10.1155/2014/408183

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 thresholdτ0is derived. When time delay is less thanτ0, 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.

Highlights

Internet worms, a great threat to the network security, can spread quickly among hosts via wired or wireless networks
(1) Considering the influence of removable devices on Internet worm propagation and the time delay caused by anomaly intrusion detection system (IDS), we propose a novel worm propagation dynamical system with time delay
In this paper, considering the influence of removable devices, a delayed worm propagation dynamical system based on anomaly IDS has been constructed

Summary

Introduction

A great threat to the network security, can spread quickly among hosts via wired or wireless networks. By considering the interaction infection between hosts and removable devices, we model a delayed worm propagation dynamical system which combines both vaccination and quarantine strategy. Local asymptotic stability of the positive equilibrium and local Hopf bifurcation are discussed to analyze the influence of time delay on worm propagation dynamical system. (1) Considering the influence of removable devices on Internet worm propagation and the time delay caused by anomaly IDS, we propose a novel worm propagation dynamical system with time delay. (2) We analyze the system stability at positive equilibrium and derive the time delay threshold at which Hopf bifurcation occurs.

Model Formulation

Stability at the Positive Equilibrium and Bifurcation Analysis

Numerical Analysis

Simulation Experiments

Conclusions