Reconstruction of the Coupling Architecture in the Ensembles of Radio-Engineering Oscillators by Their Signals Using the Methods of Granger Causality and Partial Directed Coherence

• Published in: Radiophysics and quantum electronics Vol. 63; no. 7; pp. 542 - 556
• Main Authors: Kornilov, M. V., Sysoev, I. V., Astakhova, D. I., Kulminsky, D. D., Bezruchko, B. P., Ponomarenko, V. I.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2020; Springer; Springer Nature B.V
• Subjects: Astronomy; Astrophysics and Astroparticles; Buildings; Causality; Coherence; Couplings; Hadrons; Heavy Ions; Lasers; Mathematical and Computational Physics; Methods; Nuclear Physics; Observations and Techniques; Optical Devices; Optics; Oscillators; Photonics; Physics; Physics and Astronomy; Prediction models; Quantum Optics; Remodeling, restoration, etc; Theoretical; Time series
• ISSN: 0033-8443; 1573-9120
• DOI: 10.1007/s11141-021-10078-8

In this work, we solve the problem of detecting the connectivity in the ensemble of radioengineering oscillators of chaos with a delay in the own dynamics by two widespread methods, namely, the method of Granger conditional causality and the method of partial directed coherence. Both approaches are based on the empirical predictive models. The estimates are tested for significance using the surrogate time series obtained by reordering of realizations. Several experimental time series of the dynamics of all the ensemble elements, which were obtained in various experiments where the oscillators were connected in a chain and a ring, are considered. The abilities of the methods to reveal the existing couplings and rule out false detection of the indirect interactions are considered in detail. Both methods are shown to correctly reveal the connectivity on the whole. At the same time, the number of the missed and false couplings is significantly higher than that when using the special technique which was developed earlier with allowance for additional information on the node structure. The main missed couplings refer to the case where the leading oscillator operates in the oscillatory regime with a pronounced periodic component. In this case, the Granger causality method detects nonexisting indirect couplings. On the whole, the partial directed coherence yields a greater number of false conclusions on the indirect and direct couplings. The results of both methods varied from one experiment to another even for the same coupling architecture, and the variation was more pronounced for the method of partial directed coherence.