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

TL;DR

This paper develops a mean-field theory to analyze synchronization stability in multilayer networks, providing accurate and computationally efficient assessments even for dissimilar layers, advancing understanding of complex network dynamics.

Contribution

The authors introduce a mean-field approach for multilayer network synchronization, reducing computational complexity and extending applicability to diverse and large systems.

Findings

High accuracy of the mean-field theory for similar layers

Effective assessment of stability in dissimilar layers

Quadratic computational complexity enables large system analysis

Abstract

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.