Explosive synchronization in interlayer phase-shifted Kuramoto oscillators on multiplex networks

TL;DR

This paper demonstrates that introducing a phase parameter in the interlayer coupling of multiplex Kuramoto oscillators can induce explosive synchronization, with the hysteresis width influenced by coupling strength and frequency mismatch, supported by mean-field analysis.

Contribution

It reveals that phase-shifted interlayer coupling can induce explosive synchronization in multiplex networks, extending the concept to single-layer networks with phase-shifted links.

Findings

Phase parameter induces explosive synchronization.

Hysteresis width depends on coupling strength and frequency mismatch.

Phase-shifted coupling can be used to achieve ES in networks.

Abstract

We show that an introduction of a phase parameter ($\alpha$), with $0 \le \alpha \le \pi/2$, in the interlayer coupling terms of multiplex networks of Kuramoto oscillators can induce explosive synchronization (ES) in the multiplexed layers. Along with the {\alpha} values, the hysteresis width is determined by the interlayer coupling strength and the frequency mismatch between the mirror (inter-connected) nodes. A mean-field analysis is performed to support the numerical results. Similar to the earlier works, we find that the suppression of synchronization is accountable for the origin of ES. The robustness of ES against changes in the network topology and frequency distribution is tested. Finally, taking a suggestion from the synchronized state of the multiplex networks, we extend the results to the classical concept of the single-layer networks in which some specific links are assigned a phase-shifted coupling. Different methods have been introduced in the past years to incite ES in coupled oscillators; our results indicate that a phase-shifted coupling can also be one such method to achieve ES.