Birth and stabilization of phase clusters by multiplexing of adaptive networks

TL;DR

This paper demonstrates how multiplexing in multi-layer adaptive networks can generate and stabilize diverse phase cluster patterns, which are unstable or nonexistent in single-layer networks, using theoretical analysis and simulations.

Contribution

It introduces a novel method to induce and analyze stable phase clusters in multiplex networks, extending understanding of synchronization phenomena.

Findings

Multiplexing induces stable phase clusters not present in single layers.

A spectral analysis method for multiplex Laplacian matrices is developed.

Analytic stability results for multilayer patterns are provided.

Abstract

We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuro- and social sciences, as well as biology, engineering, and other disciplines. We show by theoretical analysis and computer simulations that multiplexing in a multi-layer network with symmetry can induce various stable phase cluster states in a situation where they are not stable or do not even exist in the single layer. Further, we develop a method for the analysis of Laplacian matrices of multiplex networks which allows for insight into the spectral structure of these networks enabling a reduction to the stability problem of single layers. We employ the multiplex decomposition to provide analytic results for the stability of the multilayer patterns. As local dynamics we use the paradigmatic Kuramoto phase oscillator, which is a simple generic model and has been successfully applied in the modeling of synchronization phenomena in a wide range of natural and technological systems.