# Stochastic Kuramoto oscillators with discrete phase states

## TL;DR

This paper introduces a stochastic generalization of the Kuramoto model with discrete phase states, analyzing how phase discretization affects synchronization and oscillation quality through analytical and numerical methods.

## Contribution

It presents a novel stochastic Kuramoto model with discrete phases, bridging continuous and discrete oscillatory systems, and explores its synchronization properties.

## Key findings

- Key observables show extrema at certain discretization levels.
- Steady-state synchrony varies with phase discretization.
- Model converges to classical Kuramoto in the continuous limit.

## Abstract

We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.