Stochastic Stabilization of Malware Propagation in Wireless Sensor Network via Aperiodically Intermittent White Noise

Abstract

In this paper, we propose a novel heterogeneous model to describe the propagation dynamics of malware (viruses, worms, Trojan horses, etc.) in wireless sensor networks. Our model takes into consideration different battery-level sensor nodes contrary to existing models. In order to control the spread of malware, we design an aperiodically intermittent controller driven by white noise, which has striking advantages of lower cost and more flexible control strategy. We give a distinct condition on stability in probability one using graph-theoretical Lyapunov function and stochastic analysis method. Our results show that the nonlinear malware propagation system can be stabilized by intermittent stochastic perturbation under the intermittent time related to stochastic perturbation intensity. Our theoretical results can be applied to understand the observed mechanisms of malware and design interventions to control the spread of malware. Numerical simulations illustrate our analytical results clearly.