Coherence enhanced by detrained oscillators: Breaking $\pi$-reflection symmetry

TL;DR

This paper introduces a generalized Kuramoto model with coupled phase variables, revealing a novel symmetry-breaking mode that enhances coherence and promotes synchronization through detrained oscillators.

Contribution

It uncovers a new dynamic mode in a swarmalator system that breaks $ ext{pi}$-reflection symmetry, advancing understanding of synchronization mechanisms.

Findings

Identification of a bounded oscillatory mode breaking symmetry

Enhanced global coherence due to symmetry breaking

Confirmation of phase diagram predictions through simulations

Abstract

We study a generalized Kuramoto model in which each oscillator carries two coupled phase variables, representing a minimal swarmalator system. Assuming perfect correlation between the intrinsic frequencies associated with each phase variable, we identify a novel dynamic mode characterized by bounded oscillatory motion that breaks the $\pi$-reflection symmetry. This symmetry breaking enhances global coherence and gives rise to a non-trivial mixed state, marked by distinct degrees of ordering in each variable. Numerical simulations confirm our analytic predictions for the full phase diagram, including the nature of transition. Our results reveal a fundamental mechanism through which detrained (dynamic) oscillators can promote global synchronization, offering broad insights into coupled dynamical systems beyond the classical Kuramoto paradigm.