Dynamical Bayesian Inference of Time-evolving Interactions: From a Pair of Coupled Oscillators to Networks of Oscillators

TL;DR

This paper presents a Bayesian inference method for detecting and analyzing time-evolving interactions and synchronization in oscillatory systems, applicable to pairs and networks of oscillators, even in noisy conditions.

Contribution

It extends previous work by detailing the method with various data types and generalizing it to networks of oscillators, enabling analysis of complex, dynamic interactions.

Findings

Effective detection of time-varying synchronization and influence direction.

Successful application to electronic circuit and cardio-respiratory data.

Generalization to small networks of oscillators.

Abstract

Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. (Phys. Rev. Lett. 109 024101, 2012) introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time- evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically-generated data, data from an analog electronic circuit, and cardio-respiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.