ESTIMATION OF INTERACTION DIRECTION BETWEEN OSCILLATORY MODEL SYSTEMS IN CASE OF CLOSE COUPLING
Cite this article as:
Khorev V. S. ESTIMATION OF INTERACTION DIRECTION BETWEEN OSCILLATORY MODEL SYSTEMS IN CASE OF CLOSE COUPLING. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 2, pp. 52-60. DOI: https://doi.org/10.18500/0869-6632-2013-21-2-52-60
The task of detection statistically significant interaction, its direction and delay between time data series of two oscillatory systems in case of close coupling is investigated with nonlinear modeling approach. Numerical experiments on oscillatory model systems with different coupling function variants are used to study main dependences.
1. Arnhold J., Grassberger P., Lehnertz K., Elger C.E. A robust method for detecting interdependences: Application to intracranially recorded EEG // Physica D: Nonlinear Phenomena. 1999. Vol. 134. P. 419.
2. Quian Quiroga R., Kraskov A., Kreuz T., Grassberger P. Performance of different synchronization measures in real data: A case study on electroencephalographic signals // Phys. Rev. E. 2002. Vol. 65. 041903.
3. Smirnov D.A., Bodrov M.B., Perez Velazquez J.L., Wenneberg R.A., Bezruchko B.P. Estimation of coupling between oscillators from short time series via phase dynamics modeling: Limitations and application to EEG data // Chaos. 2005. Vol. 15. 024102.
4. Smirnov D.A., Andrzejak R.G. Detection of weak directional coupling: Phase dynamics approach versus state space approach // Phys. Rev. E. 2005. Vol. 71. 036207.
5. Пиковский А.С., Розенблюм М.Г., Куртс Ю. Синхронизация: фундаментальное нелинейное явление. М.: Техносфера, 2002.
6. Rosenblum M.G., Pikovsky A.S. Detecting direction of coupling in interacting oscillators // Phys. Rev. E. 2001. Vol. 64. 045202.
7. Smirnov D.A., Bezruchko B.P. Estimation of interaction strength and direction from short and noisy time series // Phys. Rev. E. 2003. Vol. 68. 046209.
8. Smirnov D.A., Barnikol U.B., Barnikol T.T., Bezruchko B.P., Hauptmann C., Buehrle C., Maarouf M., Sturm V., Freund H.-J., Tass P.A. The generation of Parkinsonian tremor as revealed by directional coupling analysis // Europhys. Lett. 2008. Vol. 83. 20003.
9. Mokhov I.I., Smirnov D.A. El Nino Southern Oscillation drives North Atlantic Oscillation as revealed with nonlinear techniques from climatic indices // Geophysical Research Letters. 2006. Vol. 33. 024557.
10. Smirnov D.A., Bezruchko B.P. Detection of couplings in ensembles of stochastic oscillators // Phys. Rev. E. 2009. Vol. 79. 046204.
11. Смирнов Д.А., Карпеев И.А., Безручко Б.П. Выявление связи между осцилляторами по коротким временным рядам: условие применимости метода моделирования фазовой динамики // Письма в ЖТФ. 2007. Т. 33, вып. 4. С. 19.
12. Pikovsky A.S., Rosenblum M.G., Kurths J. Phase synchronization in regular and chaotic systems // Int. J. Bifurc. Chaos. 2000. Vol. 10. P. 2291.
13. Sch ̈afer C., Rosenblum M.G., Abel H.-H., Kurths J. Synchronization in the human cardiorespiratory system //Phys. Rev. E. 1999. Vol. 60. P. 857.
14. Janson N.B., Balanov A.G., Anishchenko V.S., McClintock P.V.E. Coherence resonance versus synchronization in a periodically forced self-sustained system // Phys. Rev. E. 2002. Vol. 65. 036212.
15. Kralemann B., Cimponeriu L., Rosenblum M.G., Pikovsky A.S., and Mrowka R. Phase dynamics of coupled oscillators reconstructed from data // Physical Rev E. 2008. Vol. 77. 066205.
BibTeX
author = {Vladimir Sergeevich Khorev},
title = {ESTIMATION OF INTERACTION DIRECTION BETWEEN OSCILLATORY MODEL SYSTEMS IN CASE OF CLOSE COUPLING},
year = {2013},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {21},number = {2},
url = {https://old-andjournal.sgu.ru/en/articles/estimation-of-interaction-direction-between-oscillatory-model-systems-in-case-of-close},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2013-21-2-52-60},pages = {52--60},issn = {0869-6632},
keywords = {Close coupling,interaction,coupling direction,time delay,oscillatory systems.},
abstract = {The task of detection statistically significant interaction, its direction and delay between time data series of two oscillatory systems in case of close coupling is investigated with nonlinear modeling approach. Numerical experiments on oscillatory model systems with different coupling function variants are used to study main dependences. }}