Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling

TL;DR

This paper investigates how ensembles of noisy, bi-harmonically coupled oscillators transition between incoherence and synchrony, revealing complex behaviors including bistability, cluster formation, and noise-induced metastability.

Contribution

It provides analytical solutions for various synchronization states in bi-harmonic oscillator ensembles with noise and frequency diversity, highlighting novel transition scenarios.

Findings

Identification of supercritical and subcritical transitions

Discovery of symmetric two-cluster solutions

Noise and finite-size effects induce metastable asynchronous states

Abstract

We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder - diversity of intrinsic oscillatory frequencies and external independent noise. Based on the self-consistent formulation, we derive analytic solutions for different synchronous states. We report on various non-trivial transitions from incoherence to synchrony where possible scenarios include: simple supercritical transition (similar to classical Kuramoto model), subcritical transition with large area of bistability of incoherent and synchronous solutions, and also appearance of symmetric two-cluster solution which can coexist with regular synchronous state. Remarkably, we show that the interplay between relatively small white noise and finite-size fluctuations can lead to metastable asynchronous solution.