Interconnected Takagi-Sugeno system and fractional SIRS malware propagation model for stabilization of Wireless Sensor Networks

Abstract

This paper is devoted to investigate the dynamical behaviors of malware attack on a familiar kind of complex heterogeneous networks, namely Wireless Sensor Network, and discuss an effective immunization treatment based on fractional interconnected Takagi-Sugeno (T-S) fuzzy systems. Our approach is based on the mathematical modeling to establish a controlled fractional network-based SIRS malware propagation model that better describes the attacking behavior of malicious objects on Wireless Sensor Network. After that, we point out some qualitative properties of the proposed network-based SIRS malware propagation model such as the existence of positively invariant set, backward bifurcation and asymptotic behavior. Especially, in order to study the model's stability, we evaluate an epidemiological threshold value R0, namely basic reproductive ratio, which ensures the existence of at least one endemic equilibrium P⁎ and the local asymptotic stability of malware-free equilibrium P0. As a consequence of theoretical result, the malware-free equilibrium P0 is unstable when R0>1 and hence, the rest of this paper is to address a stabilization problem for the proposed controlled network-based model and establish some sufficient conditions related to linear matrix inequalities and positive definite matrices. Finally, we illustrate the obtained theoretical results by a computational example.