Cascading failure of interdependent networks with dependence groups obeying different distributions

Recent work on the cascading failure of networks with dependence groups assumes that the number of nodes in each dependence group is equal. In this paper, we construct a model on interdependent networks with dependence groups against cascading failure. The size of dependence group is supposed to obey the Poisson Distribution and the Truncated Normal Distribution, respectively. By applying the tools of mean-field approximation and the generating function techniques, the cascading model is theoretically analyzed and the theoretical solutions are nearly consistent with the simulation values. Besides, we define three kinds of coupling preferences based on node degree, i.e. assortative coupling, disassortative coupling and random coupling. The connection between layers is no longer one-to-one correspondence of nodes, but fully connection of some groups. In addition, some factors affecting the network robustness are discussed and extensive simulations are realized on two-layer BA networks. The simulation results show that the coupling preference has influence on the network robustness and the network with dependence groups obeying the Truncated Normal Distribution performs better than the Poisson Distribution.