Figure 1. Schematic representation of a multiplex of two layers of identical oscillators.

Labels σ and λ denote the intra- and inter-layer coupling strengths, respectively. Each node i (j) in the top (bottom) layer is an m dimensional dynamical system whose state is represented by the vector x_i (y_j). The topologies of layers X and Y are encoded in the and Laplacian matrices, respectively. Originally , but as we start deleting links, we can write where contains the links that have been deleted in the bottom layer.