Cascading failure in multilayer network with asymmetric dependence group

Cascading failure is widespread in the networks. In order to solve practical problems, it is necessary to study the cascading failure in the complex network. In this paper, we mainly focus on the cascading failure in multilayer networks with asymmetric dependence group and discuss the influence factors of networks’ robustness. We build a model with recover mechanism within the layer and define an effect between the layers. Under the effect, if the fraction of failure nodes between layers is greater than or equal to the failure–recover threshold, other connected nodes in other layers will recover and if the fraction of failure nodes between layers is less than the failure–recover threshold, the connected nodes in other layers will become invalid. It is worth mentioning that in our model, the impact of the proportion v of the dependency groups and the group size g on the robustness of the networks is related to the probability p of initial removal. Because the failure and recovery mechanism exist, the networks robustness will be reversed by changing the value of p for different values of v and g. In addition, the number of layers T has different effects on networks robustness due to the effect between the layers.