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.
@article{arxiv.1405.4126,
title = {Direct extraction of phase dynamics from fluctuating rhythmic data based on a Bayesian approach},
author = {Kaiichiro Ota and Toshio Aoyagi},
journal= {arXiv preprint arXiv:1405.4126},
year = {2014}
}