REVEALING NONLINEAR COUPLINGS BETWEEN STOCHASTIC OSCILLATORS FROM TIME SERIES
Cite this article as:
Smirnov D. A. REVEALING NONLINEAR COUPLINGS BETWEEN STOCHASTIC OSCILLATORS FROM TIME SERIES. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 2, pp. 16-38. DOI: https://doi.org/10.18500/0869-6632-2010-18-2-16-38
The problem of detection and quantitative characterization of nonlinear directional couplings between stochastic oscillators is considered. Coupling characteristics and a technique for their estimation from time series are suggested. An analytic expression for a statistical significance level of the conclusion about coupling presence is derived that allows a reliable inference from relatively short signals. Performance of the approach is demonstrated in numerical experiments with diverse individual properties of oscillators and different kinds of coupling functions.
1. Пиковский А.С., Розеблюм М.Г., Куртс Ю. Синхронизация: фундаментальное нелинейное явление. М.: Техносфера. 2003.
2. Tass P.A. Phase resetting in medicine and biology – stochastic modelling and data analysis. Berlin: Springer, 1999.
3. Boccaletti S., Kurths J., Osipov G., Valladares D., Zhou C. The synchronization of chaotic systems // Phys. Rep. 2002. Vol. 366. P. 1.
4. Mosekilde E., Maistrenko Yu., Postnov D. Chaotic Synchronization. Applications to Living Systems. Singapore: World Scientific, 2002.
5. Balanov A., Janson N., Postnov D., Sosnovtseva O. Synchronization: From Simple to Complex. Berlin: Springer-Verlag, 2008.
6. Rosenblum M.G., Pikovsky A.S. Detecting direction of coupling in interacting oscillators // Phys. Rev. E. 2001. Vol. 64, 045202(R).
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. Palus M., Stefanovska A. Direction of coupling from phases of interacting oscillators: An information-theoretic approach // Phys. Rev. E. 2003. Vol. 67, 055201.
9. Kralemann B., Cimponeriu L., Rosenblum M., Pikovsky A., Mrowka R. Uncovering interaction of coupled oscillators from data // Phys. Rev. E. 2007. Vol. 76, 055201.
10. Kralemann B., Cimponeriu L., Rosenblum M., Pikovsky A., Mrowka R. Phase dynamics of coupled oscillators reconstructed from data // Phys. Rev. E. 2008. Vol. 77, 066205.
11. Baccala L.A., Sameshima K. Partial directed coherence: a new concept in neural structure determination // Biological Cybernetics, 2001. Vol. 84. P. 463.
12. Ancona N., Marinazzo D., Stramaglia S. Radial basis function approach to nonlinear Granger causality of time series // Phys. Rev. E. 2004. Vol. 70, 056221.
13. Schreiber T. Measuring information transfer // Phys. Rev. Lett. 2000. Vol. 85. P. 461.
14. Verdes P.F. Assessing causality from multivariate time series // Phys. Rev. E. 2005. Vol. 72, 026222.
15. Hlavackova-Schindler K., Palus M., Vejmelka M., Bhattacharya J. Causality detection based on information-theoretic approaches in time series analysis // Phys. Rep. 2007. Vol. 441. P. 1.
16. Vejmelka M., Palus M. Inferring the directionality of coupling with conditional mutual information // Phys. Rev. E. 2008. Vol. 77, 026214.
17. Rosenblum M.G., Cimponeriu L., Bezerianos A., Patzak A., Mrowka R. Identification of coupling direction: Application to cardiorespiratory interaction // Phys. Rev. E. 2002. Vol. 65, 041909.
18. Prokhorov M.D., Ponomarenko V.I., Gridnev V.I., Bodrov M.B., Bespyatov A.B. Synchronization between main rhythmic processes in the human cardiovascular system // Phys. Rev. E. 2003. Vol. 68, 041913.
19. Luchinsky D.G., Millonas M.M., Smelyanskiy V.N., Pershakova A., Stefanovska A., McClintock P.V. Nonlinear statistical modeling and model discovery for cardiorespiratory data // Phys. Rev. E. 2005. Vol. 72, 021905.
20. Hramov A.E., Koronovskii A.A., Ponomarenko V.I., Prokhorov M.D. Detection of synchronization from univariate data using wavelet transform // Phys. Rev. E. 2007. Vol. 75, 056207.
21. Sosnovtseva O.V., Pavlolv A.N., Mosekilde E., Holstein-Rathlou N.H., Marsh D.J. Double-wavelet approach to study frequency and amplitude modulation in renal autoregulation // Phys. Rev. E. 2004. Vol. 70, 031915.
22. Pavlov A.N., Sosnovtseva O.V., Pavlova O.N., Mosekilde E., Holstein-RathlouN.-H. Characterizing multimode interaction in renal autoregulation // Physiological Measurements, 2008. Vol. 29. P. 945.
23. Eguia M.C., Dawson S.P., Mindlin G.B. Information transmission and recovery in neural communications channels // Phys. Rev. E. 2000. Vol.62. P. 7111.
24. Kiemel T., Gormley K., Guan L., Williams T., Cohen A. Estimating the strength and direction of functional coupling in the lamprey spinal cord // J. Computational Neuroscience. 2003. Vol. 15. P. 233.
25. Blinowska K.J., Kus R., Kaminski M. Granger causality and information flow in multivariate processes // Phys. Rev. E. 2004. Vol. 70, 050902(R).
26. Pereda E., Quian Quiroga R., Bhattacharya J. Nonlinear multivariate analysis of neurophysiological signals // Progress in Neurobiology. 2005. Vol. 77. P. 1.
27. Brea J., Russell D.F., Neiman A.B. Measuring direction in the coupling of biological oscillators: A case study for electroreceptors of paddlefish // Chaos. 2006. Vol. 16, 026111.
28. Schelter B., Winterhalder M., Eichler M., Peifer M., Hellwig B., Guschlbauer B., Luecking C., Dahlhaus R., Timmer J. Testing for directed influences among neural signals using partial directed coherence // J. Neurosci. Methods. 2005. Vol. 152. P. 210.
29. Wang S., Chen Y., Ding M., Feng J., Stein J.F., Aziz T.Z., Liu X.J. Revealing the dynamic causal interdependence between neural and muscular signals in Parkinsonian tremor // J. Franklin Institute. 2007. Vol. 344. P. 180.
30. Osterhage H., Mormann F., Wagner T., Lehnertz K. Measuring the directionality of coupling: Phase versus state space dynamics and application to EEG time series // Int. J. Neural Syst. 2007. Vol. 17. P. 139.
31. 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.
32. 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.
33. Smirnov D.A., Bezruchko B.P. Detection of couplings in ensembles of stochastic oscillators // Phys. Rev. E. 2009. Vol. 79, 046204.
34. Kori H., Kuramoto Y. Slow switching in globally coupled oscillators: robustness and occurrence through delayed coupling // Phys. Rev. E. 2001. Vol. 63, 046214.
35. Kuramoto Y. Chemical Oscillations, Waves and Turbulence. Berlin: Springer-Verlag, 1984.
36. Pikovsky A.S., Rosenblum M.G., Kurths J. Phase synchronization in regular and chaotic systems // Int. J. Bifurc. Chaos. 2000. Vol.10, No 10. P. 2291.
37. Gabor D. Theory of communication // J. Inst. Elect. Eng. (London). 1946. Vol. 93. P. 429.
38. Rosenblum M.G., Pikovsky A.S., Kurths J., Schaefer C., Tass P.A. Phase synchronization: from theory to data analysis // Neuro-informatics. Handbook of Biological Physics. Edited by F. Moss and S. Gielen. New York: Elsevier Science, 2001. P. 279.
39. Kendall M.C., Stuart A. The advanced theory of statistics. New York: Hafner, 1979.
40. Никитин Н.Н., Разевиг В.Д. Методы цифрового моделирования стохастических дифференциальных уравнений и оценка их погрешностей // Журнал выч. математики и мат. физики. 1978. Т. 18, No 1. С. 106.
41. Анищенко В.С., Вадивасова Т.Е., Окрокверцхов Г.А., Стрелкова Г.И. Статистические свойства динамического хаоса // УФН. 2005. Т. 175. С. 163.
42. Thompson J.M.T. and Stewart H.B. Nonlinear Dynamics and Chaos. New York: Wiley, 1987.
43. Morris C., Lecar H. Voltage oscillations in the barnacle giant muscle fiber // Biophys. J. 1981. Vol. 35. P. 193.
44. Izhikevich E.M. Neural excitability, spiking and bursting // Int. J. Bifurc. Chaos. 2000. Vol. 10. P. 1171.
45. Ermentrout G.B., Kopell N. Oscillator death in systems of coupled neural oscillators // SIAM J. Appl. Math. 1990. Vol. 50. P. 125.
46. Smirnov D., Schelter B., Winterhalder M., Timmer J. Revealing direction of coupling between neuronal oscillators from time series: Phase dynamics modeling versus partial directed coherence // Chaos. 2007. Vol. 17, 013111.
BibTeX
author = {D. A. Smirnov},
title = {REVEALING NONLINEAR COUPLINGS BETWEEN STOCHASTIC OSCILLATORS FROM TIME SERIES},
year = {2010},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {18},number = {2},
url = {https://old-andjournal.sgu.ru/en/articles/revealing-nonlinear-couplings-between-stochastic-oscillators-from-time-series},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2010-18-2-16-38},pages = {16--38},issn = {0869-6632},
keywords = {Сoupling estimation,Coupled oscillators,nonlinear time series analysis,phase dynamics,statistical inference},
abstract = {The problem of detection and quantitative characterization of nonlinear directional couplings between stochastic oscillators is considered. Coupling characteristics and a technique for their estimation from time series are suggested. An analytic expression for a statistical significance level of the conclusion about coupling presence is derived that allows a reliable inference from relatively short signals. Performance of the approach is demonstrated in numerical experiments with diverse individual properties of oscillators and different kinds of coupling functions. }}