Impact of field heterogeneity on the dynamics of the forced Kuramoto model

TL;DR

This paper investigates how heterogeneity in the external field affects synchronization in a system of coupled oscillators, revealing that field heterogeneity can break entrainment and induce diverse dynamical states.

Contribution

It introduces an analytical and numerical study of the forced Kuramoto model with heterogeneous fields, showing how heterogeneity disrupts synchronization at various frequencies.

Findings

Heterogeneous fields induce dynamical heterogeneity in oscillator systems.

Disruption of entrainment occurs at critical field frequencies.

Different groups can exhibit distinct disrupted dynamics.

Abstract

We studied the impact of field heterogeneity on entrainment in a system of uniformly interacting phase oscillators. Field heterogeneity is shown to induce dynamical heterogeneity in the system. In effect, the heterogeneous field partitions the system into interacting groups of oscillators that feel the same local field strength and phase. Based on numerical and analytical analysis of the explicit dynamical equations derived from the periodically forced Kuramoto model, we found that the heterogeneous field can disrupt entrainment at different field frequencies when compared to the homogeneous field. This transition occurs when the phase- and frequency-locked synchronization between groups of oscillators is broken at a critical field frequency, causing each group to enter a new dynamical state (disrupted state). Strikingly, it is shown that disrupted dynamics can differ between groups.