Estimation of the time delay of coupling between oscillators from time realizations of oscillation phases for different properties of phase dynamics

The problem of interval estimation of the time delay of the coupling between oscillatory systems from observed time series is considered. It is shown that the known asymptotic estimates based on the empirical model in the form of a system of first-order phase oscillators and the maximum likelihood f...

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Bibliographic Details
Published in:Journal of communications technology & electronics 2017-03, Vol.62 (3), p.241-250
Main Authors: Sidak, E. V., Smirnov, D. A., Bezruchko, B. P.
Format: Article
Language:English
Subjects:
Amplitudes
Approximation
Communications Engineering
Communications technology
Connectors
Diagnostic systems
Diagnostics
Dynamical systems
Dynamics
Dynamics Chaos in Radiophysics and Electronics
Engineering
Estimates
Estimating techniques
Networks
Noise
Nonlinear dynamics
Oscillators
Phases
Studies
Time
Time delay
Time series
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Summary:The problem of interval estimation of the time delay of the coupling between oscillatory systems from observed time series is considered. It is shown that the known asymptotic estimates based on the empirical model in the form of a system of first-order phase oscillators and the maximum likelihood formalism can lead to false inferences of the value of the time delay in two typical situations: 1) nonlinear low-dimensional systems whose phases are well-determined but, as a result of significant amplitude fluctuations, the phase approximation is insufficient for describing the dynamics and 2) systems whose phases are defined not quite well because of too large amplitude fluctuations. A method for empirical diagnostics of problematic situations and its modification (coarse estimation) providing a low probability of false inferences in these situation are proposed. The efficiency of the diagnostic criterion and coarse estimation suggested is demonstrated on reference systems with different dynamic properties (linear stochastic oscillators, van der Pol oscillators, and Ressler and Lorenz chaotic systems).
ISSN:1064-2269
1555-6557
DOI:10.1134/S1064226917030196