Explosive behaviour in networks of Winfree oscillators

TL;DR

This paper investigates explosive synchronization phenomena in directed networks of Winfree oscillators with diverse degree distributions and correlated intrinsic frequencies, revealing abrupt transitions explained by bifurcation analysis.

Contribution

It introduces a degree-based mean field approach to analyze explosive transitions in Winfree oscillator networks with correlated frequencies and diverse degree distributions.

Findings

Explosive transitions occur between steady states or between steady state and periodic solutions.

Bifurcation theory explains the abrupt changes in network dynamics.

The Ott/Antonsen ansatz effectively derives mean field equations for analysis.

Abstract

We consider directed networks of Winfree oscillators with power law distributed in- and out-degree distributions. Gaussian and power law distributed intrinsic frequencies are considered, and these frequencies are positively correlated with oscillators' in-degrees. The Ott/Antonsen ansatz is used to derive degree-based mean field equations for the expected dynamics of networks, and these are numerically analysed. In a variety of cases "explosive" transitions between either two different steady states or between a steady state and a periodic solution are found, and these transitions are explained using bifurcation theory.