The Research on Cascading Failure of Farey Network

Cascading failure is an important part of the dynamics in complex network. In this paper, we research the cascading failure of Farey network which is scale-free network with fractal properties by data analysis. According to the analyses, we obtain an iterative expression of the failure nodes’ number at the certain time step, anther iterative expression of the time which is needed for the network being global collapse, and the sequence of nodes failure in the Farey network. By theoretical derivation, we get an approximate solutions of perturbation threshold R to make the network achieve the global collapse. If the nodes number of the Farey network is lager, simulate results are closer to theoretical value. By the simulation, we obtain the cascading failure process of the Farey network after suffering deliberate attack and random attack. Simulation results show that, the failure nodes of Farey network increase gradually as R raises, until the network is global collapse. Moreover, Farey network shows stronger robustness for random attack. abstract environment.