文摘
Many modern systems have the property of coupling, which weakens the system against the outburst of failure. The risks to fail in a single layer may propagate to the entire system through inter-layer connections. In the field of propagation process, the existing literatures mainly focus on the global phenomena in coupled systems through some statistic methods, the dynamical evolution of failure risk propagation and the protection schemes for coupled systems are seldom mentioned. In this paper, we model the coupled systems using six types of coupled networks, over which the failure risk propagation occurs. Then, three cellular automata (CA) models are performed to describe the protection schemes in case of failure risk propagation. Based on a newly presented measurement, a series of experiments are conducted on the coupled networks as well as the single-layered networks, where the propagation processes with and without protection schemes are demonstrated. The results show that the failure risk propagation varies depending on the type and structure of the coupled networks. Moreover, with a small fraction of nodes protected based on some immunization strategies, the system’s robustness to the failure risk propagation is highly improved.