Explosive synchronization in coupled nonlinear oscillators on multiplex network

TL;DR

This paper demonstrates that explosive synchronization can occur in multiplex networks of nonlinear oscillators with mixed coupling types, and shows how noise and coupling parameters influence the transition's nature.

Contribution

It reveals the conditions under which explosive synchronization occurs in multiplex networks with mixed attractive and repulsive couplings, and how to control the transition type.

Findings

Explosive synchronization occurs with Gaussian noise in multiplex networks.

The transition is first order with hysteresis, depending on coupling and noise.

Control over the transition type is possible by tuning coupling strength and noise.

Abstract

We report the emergence of explosive synchronization in a multiplex network where oscillators on the first layer are coupled with attractive coupling and those on the second layer, coupled with repulsive coupling. With Stuart-Landau and FitzHugh-Nagumo oscillators as the nodal dynamics, we consider non-local and mean-field intralayer couplings. We establish that explosive synchronization occurs in the multiplex network in the presence of Gaussian noise, and the transition is first order with hysteresis to a state of complete intra-layer and in-phase interlayer synchronization. The width of the hysteresis depends on the range of intralayer attractive coupling, strength of interlayer coupling and noise. We also see how to have control over this induced transition so that the explosive nature, if undesirable, can be converted to continuous type by tuning the strength of repulsive coupling or noise.