# Stochastic phase-cohesiveness of discrete-time Kuramoto oscillators in a frequency-dependent tree network

arXiv: https://arxiv.org/abs/1903.09676 · HTML: https://mlsanity.com/paper/1903.09676/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2019.

## Built on by (most cited first, 1 of 1)

- [Model-Based and Data-Driven Hierarchical Control and Topology Co-Design for Robust Networked Systems](https://mlsanity.com/paper/2606.11596/) (2026)

## Abstract (arXiv)

This paper presents the notion of stochastic phase-cohesiveness based on the concept of recurrent Markov chains and studies the conditions under which a discrete-time stochastic Kuramoto model is phase-cohesive. It is assumed that the exogenous frequencies of the oscillators are combined with random variables representing uncertainties. A bidirectional tree network is considered such that each oscillator is coupled to its neighbors with a coupling law which depends on its own noisy exogenous frequency. In addition, an undirected tree network is studied. For both cases, a sufficient condition for the common coupling strength and a necessary condition for the sampling-period are derived such that the stochastic phase-cohesiveness is achieved. The analysis is performed within the stochastic systems framework and validated by means of numerical simulations.