Cascading failures on correlated interdependent networks with dependency groups

The topologies of interdependent networks markedly affect the cascading failures and phase transition. However, the effects of interlayer degree correlations on cascading failures on interdependent networks with dependency groups have not been investigated. In this paper, we propose a cascading failure model on correlated interdependent networks with dependency groups, and use a percolation theory to describe the final state of the dynamics. Through extensive numerical simulations and theoretical analysis, we find that interlayer degree correlations enhance the robustness of the system. On networks with homogeneous degree distribution, the system always exhibits a discontinuous phase transition. However, on networks with heterogeneous degree distributions, the phase transition is continuous (discontinuous) for strong (weak) interlayer degree correlations. The theoretical and numerical predictions agree well with each other.