Cascading failures in multiplex network under flow redistribution

Understanding the robustness of real-world complex systems is a key step to design reliable systems and maintain their stability and normal functions. In this paper, we propose a flow redistribution model in two-layer multiplex network and study its cascading dynamics, where an initial edge failure may cause large cascading failure through the network. In our model, initially an edge on layer A fails and a proportion a of flow on the edge is redistributed to the overlap link in layer B if there exists one, while the remaining (1−a) proportion of flow is redistributed under a local weighted flow redistribution rule. Similarly a proportion b of flow of a failed edge in layer B is redistributed to the overlap link in layer A. The cascading failure continues until a steady state is reached. We analytically calculate the resilience threshold of the network and validate it by numerical simulations. We firstly find that there is an optimal weighting of edge flow at which the robustness of the system is the highest. Then we find that for the two coupled layers of networks with obviously different resilience, the layer with smaller resilience benefits from the coupled system while the robustness of the layer with larger resilience is damaged due to inter-layer cascading process. The coupled system is the most robust when the inter-layer degree correlation is maximally positive.