Determining the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations

TL;DR

This paper derives an analytical expression for the critical coupling in explosive synchronization of Kuramoto oscillators on scale-free networks, highlighting the inverse relationship with average degree and validating results through simulations.

Contribution

It introduces a mean-field approximation to determine the critical coupling for explosive synchronization in scale-free networks, revealing a new inverse dependence on average degree.

Findings

Critical coupling inversely proportional to average degree.

Derived equation differs from unimodal frequency distribution cases.

Numerical simulations confirm analytical predictions.

Abstract

Explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. In the current work, we took into account mean-field approximations to determine the critical coupling of such explosive synchronization. The obtained equation for the critical coupling has an inverse dependence with the network average degree. This expression differs from that calculated when the frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. We also conducted numerical simulations to verify our analytical results.