For citation:
Kornilov M. V., Sysoev I. V. Investigating nonlinear granger causality method efficiency at strong synchronization of systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, vol. 22, iss. 4, pp. 66-76. DOI: 10.18500/0869-6632-2014-22-4-66-76
Investigating nonlinear granger causality method efficiency at strong synchronization of systems
Detecting the direction of coupling between systems using records of their oscillations is an actual task for many areas of knowledge. Its solution can hardly be achieved in case of synchronization. Granger causality method is promising for this task, since it allows to hope for success in the case of partial (e.g., phase) synchronization due to considering not only phases but also amplitudes of both signals. In this paper using the etalon test systems with pronounced time scale the method of nonlinear Granger causality was shown to be effective even in the case of strong phase-locking, with phase synchronization index up to 0.95. Obtained results were tested for significance by various methods based on surrogates times series generation, which showed similar estimates.
- Baccala LA, Sameshima K. Partial directed coherence: a new concept in neural structure determination. Biol. Cybern. 2001;84(6):463—474. DOI: 10.1007/PL00007990.
- Schreiber T. Measuring information transfer. Phys. Rev. Lett. 2000;85(2):461—464. DOI: 10.1103/PhysRevLett.85.461.
- Rosenblum M, Pikovsky A. Detecting direction of coupling in interacting oscillators. Phys. Rev. E. 2001;64(4):045202. DOI: 10.1103/PhysRevE.64.045202.
- Smirnov D, Bezruchko B. Estimation of interaction strength and direction from short and noisy time series. Phys. Rev. E. 2003;68(4):046209. DOI: 10.1103/PhysRevE.68.046209.
- Granger CWJ. Investigating causal relations by econometric models and cross-spectral methods. Econometrica. 1969;37(3):424—438. DOI: 10.2307/1912791.
- Baccala LA, Sameshima K, Ballester G, Do Valle AC, Timo-Laria C. Studying the interactions between brain structures via directed coherence and Granger causality. Applied Signal Processing. 1998;5(1):40—48. DOI: 10.1007/s005290050005.
- Gourevitch B, Le Bouquin-Jeannes R, Faucon G. Linear and nonlinear causality between signals: methods, examples and neurophysiological applications. Biol. Cybern. 2006;95(4):349—369. DOI: 10.1007/s00422-006-0098-0.
- Tass P, Smirnov D, Karavaev A, Barnikol U, Barnikol T, Adamchic I, Hauptmann C, Pawelcyzk N, Maarouf M, Sturm V, Freund HJ, Bezruchko B. The causal relationship between subcortical local field potential oscillations and Parkinsonian resting tremor. J. Neural Eng. 2010;7(1):016009. DOI: 10.1088/1741-2560/7/1/016009.
- Mokhov II, Smirnov DA. Empirical estimates of the influence of natural and anthropogenic factors on the global surface temperature. Doklady Earth Science. 2009;427(1):798–803. DOI: 10.1134/S1028334X09050201.
- Kornilov MV, Sysoev IV. Influence of the choice of the model structure for working capacity of nonlinear granger causality approach. Izvestiya VUZ. Applied Nonlinear Dynamics. 2013;21(2):74—87 (in Russian). DOI: 10.18500/0869-6632-2013-21-2-74-87.
- Allefeld C, Kurths J. Testing for phase synchronization. Int. J. Bifurc. Chaos. 2004;14(2):405—416. DOI: 10.1142/S021812740400951X.
- Packard N, Crutchfield J, Farmer J, Shaw R. Geometry from a time series. Phys. Rev. Lett. 1980;45(9):712—716. DOI: 10.1103/PhysRevLett.45.712.
- Kougioumtzis D. State space reconstruction parameters in the analysis of chaotic time series – the role of the time window length. Physica D. 1996;95(1):13—28. DOI: 10.1016/0167-2789(96)00054-1.
- Rossler OE. An equation for continuous chaos. Phys. Lett. A. 1976;57(5):397—398. DOI: 10.1016/0375-9601(76)90101-8.
- Kiyashko SV, Pikovsky AS, Rabinovich MI. Automatic radio range generator with stochastic behavior. J. Commun. Technol. Electron. 1980;25(2):336—343 (in Russian).
- Kornilov MV, Golova TM, Sysoev IV. Selection of the temporal scales of the prognostic model used to evaluate connectivity by the Granger nonlinear causality method. In: Abstracts of Reports of the VIII All-Russian Conference of Young Scientists «Nanoelectronics, Nanophotonics and Nonlinear Physics». 3–5 September Saratov 2013. Saratov: Saratov University Publishing; 2013. P. 128—129 (in Russian).
- Schreiber T, Schmitz A. Improved surrogate data for nonlinearity tests. Phys. Rev. Lett. 1996;77(22):635—638. DOI: 10.1103/PhysRevLett.77.635.
- Dolan KT, Neiman A. Surrogate analysis of coherent multichannel data. Phys. Rev. E. 2002;65(2):026108. DOI: 10.1103/PhysRevE.65.026108.
- Thiel M, Romano MC, Kurths J, Rolfs M and Kliegl R. Twin surrogates to test for complex synchronization. Europhys. Lett. 2006;75(4):535—541. DOI: 10.1209/epl/i2006-10147-0.
- 1839 reads