Transition from localized to mean field behaviour of cascading failures in the fiber bundle model on complex networks

We study the failure process of fiber bundles on complex networks focusing on the effect of the degree of disorder of fibers' strength on the transition from localized to mean field behaviour. Starting from a regular square lattice we apply the Watts-Strogatz rewiring technique to introduce long range random connections in the load transmission network and analyze how the ultimate strength of the bundle and the statistics of the size of failure cascades change when the rewiring probability is gradually increased. Our calculations revealed that the degree of strength disorder of nodes of the network has a substantial effect on the localized to mean field transition. In particular, we show that the transition sets on at a finite value of the rewiring probability, which shifts to higher values as the degree of disorder is reduced. The transition is limited to a well defined range of disorder, so that there exists a threshold disorder of nodes' strength below which the randomization of the network structure does not provide any improvement neither of the overall load bearing capacity nor of the cascade tolerance of the system. At low strength disorder the fully random network is the most stable one, while at high disorder best cascade tolerance is obtained at a lower structural randomness. Based on the interplay of the network structure and strength disorder we construct an analytical argument which provides a reasonable description of the numerical findings.Comment: 30 pages, 11 figure