Study on cascading invulnerability of multi-coupling-links coupled networks based on time-delay coupled map lattices model

Abstract

The couplings among different networks facilitate their communications, while at the same time they also bring the risk of enhancing the wide spread of cascading failures to the coupled networks. Given that there is usually the time-delay during the spread of failures and more than one coupling link a node might possess, a cascading failure model for scale-free multi-coupling-link coupled networks is built in this paper, based on time-delay coupled map lattices (CML) model, which may be wider representative than previous models. Our research shows that in BA (Barabási-Albert) scale-free coupled networks, there is a threshold hT ≈ 3: when the coupling strength is bellow this threshold, the stronger coupling strength corresponds to a lower invulnerability; and vice versa, the stronger coupling strength would bring a higher invulnerability. In addition, our studies show that the presence of time-delay not only prolongs the failure spreading time during which measures can be taken to suppress cascading failures, but also has a significant influence on the eventual cascading size, for detail, if intra-layer time-delay τ1 and inter-layer time-delay τ2 can have any values, then the multiples of the two numbers will cause larger cascading size. We hope our research can provide a reference for building high-invulnerable coupled networks or the increase of the invulnerability of the coupled networks.