Percolation-cascading in multilayer heterogeneous network with different coupling preference

Multilayer network with different coupling preference is often used to study complex systems. In this paper we mainly focus on percolation-cascading process in multilayer heterogeneous networks including BA-BA, ER-ER, BA-ER. We put forward our percolation-cascading model and from calculation of Xn and Zn we can get resulting size of mutual largest component in different layers. Refer to Newman's definition of assortativity we design a stochastic structural algorithm to generate dependency edges between layers from which we get networks with different coupling coefficient. Simulation shows that assortative network in percolation-cascading process performs better and when the layers of multilayer network meet with BA network the robustness of the network increases.