Multiplexing induced explosive synchronization in Kuramoto oscillators with inertia

TL;DR

This paper demonstrates that multiplex networks of second-order Kuramoto oscillators can exhibit explosive synchronization without frequency-degree correlation, and that multiplexing can induce and control ES in layers.

Contribution

It reveals that multiplexing induces explosive synchronization in second-order Kuramoto oscillators, even without natural frequency-degree correlation, and shows how inter-layer coupling controls this transition.

Findings

Multiplexing supports first-order synchronization in homogeneous layers.

Heterogeneous layers can exhibit ES due to multiplexing with homogeneous layers.

ES transition can be controlled by coupling strengths.

Abstract

Explosive synchronization (ES) of coupled oscillators on networks is shown to be originated from existence of correlation between natural frequencies of oscillators and degrees of corresponding nodes. Here, we demonstrate that ES is a generic feature of multiplex network of second-order Kuramoto oscillators and can exist in absence of a frequency-degree correlation. A monoplex network of second-order Kuramoto oscillators bearing homogeneous (heterogeneous) degree-distribution is known to display the first-order (second-order) transition to synchronization. We report that multiplexing of two such networks having homogeneous degree-distribution support the first-order transition in both the layers thereby facilitating ES. More interesting is the multiplexing of a layer bearing heterogeneous degree-distribution with another layer bearing homogeneous degree-distribution, which induces a first-order (ES) transition in the heterogeneous layer which was incapable of showing the same in the isolation. Further, we report that such induced ES transition in the heterogeneous layer of multiplex networks can be controlled by varying inter and intra-layer coupling strengths. Our findings emphasize on importance of multiplexing or impact of one layer on dynamical evolution of other layers of systems having inherent multiplex or multilevel architecture.