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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| Veröffentlicht in: | Journal of communications technology & electronics 2017-03, Vol.62 (3), p.241-250 |
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| container_title | Journal of communications technology & electronics |
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| creator | Sidak, E. V. Smirnov, D. A. Bezruchko, B. P. |
| description | 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). |
| doi_str_mv | 10.1134/S1064226917030196 |
| format | Article |
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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).</description><identifier>ISSN: 1064-2269</identifier><identifier>EISSN: 1555-6557</identifier><identifier>DOI: 10.1134/S1064226917030196</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>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</subject><ispartof>Journal of communications technology & electronics, 2017-03, Vol.62 (3), p.241-250</ispartof><rights>Pleiades Publishing, Inc. 2017</rights><rights>COPYRIGHT 2017 Springer</rights><rights>Journal of Communications Technology and Electronics is a copyright of Springer, 2017.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c459t-4dc4ee71165db150098604169a19c21aa78e3f0818dfe36c428c973103ca2aa83</citedby><cites>FETCH-LOGICAL-c459t-4dc4ee71165db150098604169a19c21aa78e3f0818dfe36c428c973103ca2aa83</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S1064226917030196$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1064226917030196$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Sidak, E. 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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. 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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).</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1064226917030196</doi><tpages>10</tpages></addata></record> |
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| 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 |
| title | Estimation of the time delay of coupling between oscillators from time realizations of oscillation phases for different properties of phase dynamics |
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