Nature of the Volcano Transition in the Fully Disordered Kuramoto Model

TL;DR

This paper investigates the volcano transition in a fully connected Kuramoto model with random interactions, using the dynamical cavity method to analyze the transition and its connection to an oscillator glass phase.

Contribution

It provides an analytical and numerical study of the volcano transition in a disordered Kuramoto model, clarifying its nature and relation to oscillator glass phases.

Findings

Identifies the conditions for the volcano transition.

Links the transition to the emergence of an oscillator glass phase.

Provides a detailed analytical framework for the transition.

Abstract

Randomly coupled phase oscillators may synchronize into disordered patterns of collective motion. We analyze this transition in a large, fully connected Kuramoto model with symmetric but otherwise independent random interactions. Using the dynamical cavity method we reduce the dynamics to a stochastic single-oscillator problem with self-consistent correlation and response functions that we study analytically and numerically. We clarify the nature of the volcano transition and elucidate its relation to the existence of an oscillator glass phase.