Revealing the failure-recovery propagation dynamics in adaptive networks

The propagation of failures in networked systems with recovery mechanism can be modeled as failure-recovery propagation processes in complex networks. Considering the adaptive response of nodes against failures, here we study the failure-recovery propagation dynamics in adaptive networks, where an active node intentionally rewires its links to improve its local external environment to reduce failure. We use the effective-degree approach and numerical simulations to analyze the dynamics of adaptive networks. In both synthetic networks and real-world networks, it is found that compared with the static networks where the first-order transition and hysteresis loop exist, the failure-recovery dynamics in adaptive networks exhibits a hysteresis loop in a much smaller parameter region of the failure rates, and with the increase of rewiring rate, the phase transition becomes continuous and the hysteresis loop disappears. This implies an opposite effect of rewiring to that in epidemic dynamics where the first-order transition and hysteresis loops are induced by adaptive rewiring. Counter-intuitively, the adaptive rewiring behaviors do not necessarily result in a reduction in the systems failure size, but even lead to an increase in the failure size of the system. There exists an optimal rewiring rate at which a minimal failure size can be achieved.