Effects of collapse probability on cascading failure dynamics for duplex weighted networks

This paper proposes a novel cascading failure dynamics model for duplex weighted network with unequal flow distribution between layers and taking into account the collapse probability of overloaded nodes. Firstly, the parameter of failure elasticity is introduced to the redundancy capacity of the nodes to carry the load, and the expressions for the tolerance threshold of the entire network in different cases are derived. In addition, the cascading failure processes caused by different deliberate attack strategies are simulated on idealized networks and the IEEE39 network, respectively. Inflection points for the effectiveness of the two attack strategies are obtained, and tolerance thresholds of the theoretical calculations are compared and analyzed with the results of the numerical simulations. Meanwhile, our results indicate that the collapse probability and the redistribution rule are vital in the vulnerability of the network, and the protection mechanism is more effective against attacks on the node of lowest load. Finally, the duplex network becomes more robust as the parameter of failure elasticity increases. Furthermore, the tolerance threshold of the networks presents an ascending trend after dropping initially as the inter-layer distribution proportion increases, and the trend of the numerical simulation is consistent with the theoretical analysis.