Inter-layer adaptation induced explosive synchronization in multiplex networks

TL;DR

This paper demonstrates that inter-layer adaptive coupling in multiplex networks induces explosive synchronization with hysteresis, regardless of individual layer architecture, highlighting multiplexing's role in synchronization phenomena.

Contribution

It introduces a novel inter-layer adaptive coupling scheme that induces explosive synchronization in multiplex networks, supported by analytical and numerical validation.

Findings

Inter-layer adaptive coupling causes explosive synchronization with hysteresis.

Hysteresis depends on inter-layer coupling strength and frequency mismatch.

Analytical results match numerical simulations, explaining the suppression of giant cluster formation.

Abstract

It is known that intra-layer adaptive coupling among connected oscillators instigates explosive synchronization (ES) in multilayer networks. Taking an altogether different cue in the present work, we consider inter-layer adaptive coupling in a multiplex network of phase oscillators and show that the scheme gives rise to ES with an associated hysteresis irrespective of the network architecture of individual layers. The hysteresis is shaped by the inter-layer coupling strength and the frequency mismatch between the mirror nodes. We provide rigorous mean-field analytical treatment for the measure of global coherence and manifest they are in a good match with respective numerical assessments. Moreover, the analytical predictions provide a complete insight into how adaptive multiplexing suppresses the formation of a giant cluster, eventually giving birth to ES. The study will help in spotlighting the role of multiplexing in the emergence of ES in real-world systems represented by multilayer architecture. Particularly, it is relevant to those systems which have limitations towards change in intra-layer coupling strength.