Synchronization in Delayed Multiplex Networks

TL;DR

This paper investigates how multiplexing and delays influence phase synchronization in complex networks, revealing conditions under which global synchrony emerges or transitions occur, depending on network architecture and coupling strength.

Contribution

It demonstrates that multiplexing and delays can induce global synchronization and alter dynamical behavior in layered networks, a novel insight into network synchronization mechanisms.

Findings

Multiplexing induces global synchronization in sparse networks at strong couplings.

Delay can enable synchronization in networks that are unsynchronized without delay.

Multiplexing can cause transitions from chaotic or quasi-periodic to periodic dynamics.

Abstract

We study impact of multiplexing on the global phase synchronizability of different layers in the delayed coupled multiplex networks. We find that at strong couplings, the multiplexing induces the global synchronization in sparse networks. The introduction of global synchrony depends on the connection density of the layers being multiplexed, which further depends on the underlying network architecture. Moreover, multiplexing may lead to a transition from a quasi-periodic or chaotic evolution to a periodic evolution. For the periodic case, the multiplexing may lead to a change in the period of the dynamical evolution. Additionally, delay in the couplings may bring upon synchrony to those multiplex networks which do not exhibit synchronization for the undelayed evolution. Using a simple example of two globally connected layers forming a multiplex network, we show how delay brings upon a possibility for the inter layer global synchrony, that is not possible for the undelayed evolution.