Effect of Perturbation and Topological Structure on Synchronization Dynamics in Multilayer Networks

TL;DR

This paper investigates how heterogeneity in link weights, based on node reputation, affects synchronization dynamics in multilayer networks, revealing that intra-layer perturbations and inter-layer variations differently influence network stability and synchronization time.

Contribution

It introduces a model considering heterogeneous link weights in multiplex networks and analyzes their effects on synchronization and structural properties, contrasting with previous models assuming uniform weights.

Findings

Intra-layer link weight perturbations alter algebraic connectivity.

Variation in inter-layer weights significantly impacts synchronization stability.

Heterogeneous weights lead to different synchronization behaviors than uniform models.

Abstract

The way the topological structure transforms from a decoupled to a coupled state in multiplex networks has been extensively studied through both analytical and numerical approaches, often utilizing models of artificial networks. These studies typically assume uniform interconnections between layers to simplify the analytical treatment of structural properties in multiplex networks. However, this assumption is not applicable for real networks, where the heterogeneity of link weights is an intrinsic characteristic. Therefore, in this paper, link weights are calculated considering the node's reputation and the impact of the inter-layer link weights are assessed on the overall network's structural characteristics. These characteristics include synchronization time, stability of synchronization, and the second-smallest eigenvalue of the Laplacian matrix (algebraic connectivity). Our findings reveal that the perturbation in link weights (intra-layer) causes a transition in the algebraic connectivity whereas variation in inter-layer link weights has a significant impact on the synchronization stability and synchronization time in the multiplex networks. This analysis is different from the predictions made under the assumption of equal inter-layer link weights.