Mean-field nature of synchronization stability in networks with multiple interaction layers

The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of synchronization in dynamical systems. However, the resulting equations are computationally expensive, and therefore difficult, if not impossible, to solve for large systems. To bridge this gap, we develop a mean-field theory of synchronization for networks with multiple interaction layers. By assuming quasi-identical layers, we obtain accurate assessments of synchronization stability that are comparable with the exact results. In fact, the accuracy of our theory remains high even for networks with very dissimilar layers, thus posing a general question about the mean-field nature of synchronization stability in multilayer networks. Moreover, the computational complexity of our approach is only quadratic in the number of nodes, thereby allowing the study of systems whose investigation was thus far precluded. Multilayer networks can achieve synchronization, both for homogeneous and heterogeneous layers, whose dynamics is described by a system of equations often computationally complex and expensive. Here, the authors propose a mean-field approach for estimating the stability of the synchronized state of multilayer networks and show this applies to both homogeneous and heterogeneous layers, lowering computational complexity