# Direct extraction of phase dynamics from fluctuating rhythmic data based on a Bayesian approach

arXiv: https://arxiv.org/abs/1405.4126 · HTML: https://mlsanity.com/paper/1405.4126/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2014.

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

- [Uncertainty-Aware Sparse Identification of Dynamical Systems via Bayesian Model Averaging](https://mlsanity.com/paper/2604.10854/) (2026)

## Abstract (arXiv)

Employing both Bayesian statistics and the theory of nonlinear dynamics, we present a practically efficient method to extract a phase description of weakly coupled limit-cycle oscillators directly from time series observed in a rhythmic system. As a practical application, we numerically demonstrate that this method can retrieve all the interaction functions from the fluctuating rhythmic neuronal activity exhibited by a network of asymmetrically coupled neurons. This method can be regarded as a type of statistical phase reduction method that requires no detailed modeling, and as such, it is a very practical and reliable method in application to data-driven studies of rhythmic systems.