Inference of Time-Evolving Coupled Dynamical Systems in the Presence of Noise

TL;DR

This paper presents a Bayesian inference-based method for analyzing time-evolving interactions in coupled oscillators, effectively distinguishing genuine dynamics from noise and tracking parameter changes over time.

Contribution

It introduces a novel phase dynamics approach that incorporates prior knowledge to infer evolving coupling functions and parameters in noisy, time-dependent systems.

Findings

Successfully distinguishes noise-induced slips from true synchronization.

Tracks the evolution of coupling functions over time.

Applied to cardiorespiratory data to reveal dynamic interactions.

Abstract

A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of the coupling functions and other parameters to be followed. It is based on phase dynamics, with Bayesian inference of the time-evolving parameters achieved by shaping the prior densities to incorporate knowledge of previous samples. The method is tested numerically and applied to reveal and quantify the time-varying nature of cardiorespiratory interactions.