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

15 pages, 13 figures, published in Physical Review E

References in corpus (9)

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• Inference of a nonlinear stochastic model of the cardiorespiratory interaction
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• Reconstruction of a random phase dynamics network from observations
• Time-varying coupling functions: dynamical inference and cause of synchronization transitions
• Estimating asymptotic phase and amplitude functions of limit-cycle oscillators from time series data
• Delta-alpha cross-frequency coupling for different brain regions
• Setting of the Poincaré section for accurately calculating the phase of rhythmic spatiotemporal dynamics
• Extracting phase coupling functions between collectively oscillating networks directly from time-series data
• Dissimilarity between synchronization processes on networks