Delay Regulated Explosive Synchronization in Multiplex Networks

TL;DR

This paper demonstrates how time delay in one layer of a multiplex network can control the type of synchronization transition, including explosive synchronization, across all layers, offering insights into complex multilayer systems with communication delays.

Contribution

It reveals that time delay in a single layer can govern synchronization transitions in all layers of a multiplex network, enabling control over explosive or continuous synchronization.

Findings

Time delay induces different synchronization transitions in a layer.

Delay in one layer influences all layers' synchronization behavior.

Control over synchronization type is possible through delay tuning.

Abstract

It is known that explosive synchronization (ES) in an isolated network of Kuramoto oscillators with inertia is significantly enhanced by the presence of time delay. Here we show that time delay in one layer of the multiplex network governs the transition to synchronization and ES in the other layers. We found that a single layer with time-delayed intra-layer coupling, depending on the values of time delay, experiences a different type of transition to synchronization, e.g., ES or continuous, and the same type of transition is incorporated simultaneously in other layer(s) as well. Hence, a suitable choice of time-delay in only one layer can lead to a desired (either ES or continuous) transition simultaneously in the delayed and other undelayed layers of multiplexed network. These results offer a platform for a better understanding of the dynamics of those complex systems which are represented by multilayered framework and contain time delays in the communication processes.