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

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.

💡 Research Summary

The paper introduces a novel Bayesian framework for inferring the time‑varying interaction structure of coupled oscillatory systems directly from their observed signals, even when the data are corrupted by stochastic noise. The authors start from a phase‑reduction description, representing each oscillator by a phase variable ϕ_i(t) and modeling its dynamics as

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