For citation:
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: 10.18500/0869-6632-2013-21-2-52-60
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 140)
Language:
Russian
Article type:
Article
UDC:
530.18
Estimation of interaction direction between oscillatory model systems in case of close coupling
Autors:
Khorev Vladimir Sergeevich, Innopolis University
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.
Reference:
- Arnhold J, Grassberger P, Lehnertz K, Elger CE. A robust method for detecting interdependences: Application to intracranially recorded EEG. Physica D: Nonlinear Phenomena. 1999;134(4):419–430.
- 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;65(4):041903. DOI: 10.1103/PhysRevE.65.041903
- Smirnov DA, Bodrov MB, Perez Velazquez JL, Wenneberg RA, Bezruchko BP. Estimation of coupling between oscillators from short time series via phase dynamics modeling: Limitations and application to EEG data. Chaos. 2005;15(2):024102. DOI: 10.1063/1.1938487
- Smirnov DA, Andrzejak RG. Detection of weak directional coupling: Phase dynamics approach versus state space approach. Phys. Rev. E. 2005;71(3):036207. DOI:10.1103/PhysRevE.71.036207
- Pikovsky AS, Rosenblum MG, Kurts Yu. Synchronization: a fundamental nonlinear phenomenon. Moscow: Tehnosphera; 2003. 496 p. (In Russian).
- Rosenblum MG, Pikovsky AS. Detecting direction of coupling in interacting oscillators. Phys. Rev. E. 2001;64(4):045202–045206. DOI: 10.1103/PhysRevE.64.045202
- Smirnov DA, Bezruchko BP. Estimation of interaction strength and direction from short and noisy time series. Phys. Rev. E. 2003;68(4):046209–10. DOI:10.1103/PhysRevE.68.046209
- Smirnov DA, Barnikol UB, Barnikol TT, Bezruchko BP, Hauptmann C, Buehrle C, Maarouf M, Sturm V, Freund H-J, Tass PA. The generation of Parkinsonian tremor as revealed by directional coupling analysis. Europhys. Lett. 2008;83(2):20003. DOI: 10.1209/0295-5075/83/20003
- Mokhov II, Smirnov DA. El Nino Southern Oscillation drives North Atlantic Oscillation as revealed with nonlinear techniques from climatic indices. Geophysical Research Letters. 2006;33(3):024557. DOI:10.1029/2005GL024557
- Smirnov DA, Bezruchko BP. Detection of couplings in ensembles of stochastic oscillators. Phys. Rev. E. 2009;79(4):046204. DOI:10.1103/PhysRevE.79.046204
- Smirnov DA, Karpeev IA, Bezruchko BP. Detection of coupling between oscillators from their short time series: Condition of applicability of the method of phase dynamics modeling. Technical Physics Letters. 2007;33(2):147-150. DOI 10.1134/S1063785007020162.
- Pikovsky AS, Rosenblum MG, Kurths J. Phase synchronization in regular and chaotic systems. Int. J. Bifurc. Chaos. 2000;10(10):2291–2305. DOI:10.1142/S0218127400001481
- Schafer C, Rosenblum MG, Abel H-H, Kurths J. Synchronization in the human cardiorespiratory system. Phys. Rev. E. 1999;60(1):857–870. DOI: 10.1103/physreve.60.857
- Janson NB, Balanov AG, Anishchenko VS, McClintock PVE. Coherence resonance versus synchronization in a periodically forced self-sustained system. Phys. Rev. E. 2002;65(3):036212.
- Kralemann B, Cimponeriu L, Rosenblum MG, Pikovsky AS, Mrowka R. Phase dynamics of coupled oscillators reconstructed from data. Physical Rev E. 2008;77(6):066205. DOI: 10.1103/PhysRevE.77.066205.
Received:
12.11.2012
Accepted:
12.11.2012
Published:
31.07.2013
Journal issue:
Short text (in English):
(downloads: 79)
- 1742 reads