Synchronization of coupled noisy oscillators: Coarse-graining from continuous to discrete phases

TL;DR

This paper investigates how continuous phase oscillators can be approximated by discrete Markov models, identifying the minimum number of states needed for accurate synchronization modeling.

Contribution

It provides conditions and criteria for coarse-graining continuous oscillators into discrete states, specifically for Kuramoto-like systems, to justify their use in synchronization studies.

Findings

Derived conditions for coarse-graining continuous phases into discrete states.

Identified the minimum number of states needed for accurate modeling.

Clarified the relationship between continuous and discrete oscillator models.

Abstract

The theoretical description of synchronization phenomena often relies on coupled units of continuous time noisy Markov chains with a small number of states in each unit. It is frequently assumed, either explicitly or implicitly, that coupled discrete-state noisy Markov units can be used to model mathematically more complex coupled noisy continuous phase oscillators. In this work we explore conditions that justify this assumption by coarse-graining continuous phase units. In particular, we determine the minimum number of states necessary to justify this correspondence for Kuramoto-like oscillators.