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Time scale synchronization of chaotic oscillators. (English) Zbl 1093.37010
Summary: This paper presents the result of the investigation of chaotic oscillator synchronization. A new approach to detect the synchronized behaviour of chaotic oscillators is proposed. This approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators. The approach is applied for the coupled Rössler and Lorenz systems.

37D45Strange attractors, chaotic dynamics
37M10Time series analysis (dynamical systems)
34C15Nonlinear oscillations, coupled oscillators (ODE)
34C28Complex behavior, chaotic systems (ODE)
Full Text: DOI
[1] Parlitz, U.; Junge, L.; Lauterborn, W.: Experimental observation of phase synchronization. Phys. rev. E 54, No. 2, 2115-2117 (1996)
[2] Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.: Experimental evidence of frequenct entrainment between coupled chaotic oscillators. Phys. rev. E 57, No. 3, 3649-3651 (1998)
[3] Allaria, E.; Arecchi, F. T.; Garbo, A. D.; Meucci, R.: Synchronization of homoclinic chaos. Phys. rev. Lett. 86, No. 5, 791-794 (2001)
[4] Ticos, C. M.; Rosa, E.; Pardo, W. B.; Walkenstein, J. A.; Monti, M.: Experimental real-time phase synchronization of a paced chaotic plasma discharge. Phys. rev. Lett. 85, No. 14, 2929 (2000) · Zbl 1182.76968
[5] Rosa, E.; Pardo, W. B.; Ticos, C. M.; Wakenstein, J. A.; Monti, M.: Phase synchronization of chaos in a plasma discharge tube. Int. J. Bifurc. chaos 10, No. 11, 2551-2563 (2000) · Zbl 1182.76968
[6] Trubetskov, D. I.; Khramov, A. E.: Synchronization of a chaotic self-oscillations in the ”spiral electronic beam --- counterpropagating electromagnetic wave” distributed system. J. commun. Technol. electron. 48, No. 1, 105-113 (2003)
[7] Tass, P. A.: Detection of n:m phase locking from noisy data: application to magnetoencephalography. Phys. rev. Lett. 81, No. 15, 3291-3294 (1998)
[8] Anishchenko, V. S.; Balanov, A. G.; Janson, N. B.; Igosheva, N. B.; Bordyugov, G. V.: Entrainment between heart rate and weak nonlinear forcing. Int. J. Bifurc. chaos 10, No. 10, 2339-2348 (2000) · Zbl 0964.92010
[9] Prokhorov: Synchronization between Main rhytmic processes in the human cardiovascular system. Phys. rev. E 68, 041913 (2003)
[10] Elson, R. C.: Synchronous behavior of two coupled biological neurons. Phys. rev. Lett. 81, No. 25, 5692-5695 (1998)
[11] Rulkov, N. F.: Modeling of spiking-bursting neural behavior using two-dimensional map. Phys. rev. E 65, 041922 (2002) · Zbl 1244.34077
[12] Tass, P. A.: Synchronization tomography: A method for three-dimensional localization of phase synchronized neuronal populations in the human brain using magnetoencephalography. Phys. rev. Lett. 90, No. 8, 088101 (2003)
[13] Pikovsky, A.; Rosenblum, M.; Kurths, J.: Synhronization: A universal concepr in nonlinear sciences. (2001) · Zbl 0993.37002
[14] Anshchenko, V. S.; Astakhov, V.; Neiman, A.; Vadivasova, T.; Schimansky-Geier, L.: Nonlinear dynamics of chaotic and stochastic systems. Tutorial and modern developments. (2001) · Zbl 1125.37001
[15] Pikovsky, A.; Rosenblum, M.; Kurths, J.: Phase synchronisation in regular and chaotic systems. Int. J. Bifurc. chaos 10, No. 10, 2291-2305 (2000) · Zbl 1090.37508
[16] Anishchenko, V. S.; Vadivasova, T. E.: Synchronization of self -- oscillations and noise -- induced oscillations. J. commun. Technol. electron. 47, No. 2, 117-148 (2002)
[17] Pecora, L. M.; Carroll, T. L.: Synchronisation in chaotic systems. Phys. rev. Lett. 64, No. 8, 821-824 (1990) · Zbl 0938.37019
[18] Pecora, L. M.; Carroll, T. L.: Driving systems with chaotic signals. Phys. rev. A 44, No. 4, 2374-2383 (1991)
[19] Murali, K.; Lakshmanan, M.: Drive-response scenario of chaos syncronization in identical nonlinear systems. Phys. rev. E 49, No. 6, 4882-4885 (1994)
[20] Murali, K.; Lakshmanan, M.: Transmission of signals by synchronization in a chaotic van der Pol-Duffing oscillator. Phys. rev. E 48, No. 3, R1624-R1626 (1994)
[21] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J.: From phase to lag synchronization in coupled chaotic oscillators. Phys. rev. Lett. 78, No. 22, 4193-4196 (1997) · Zbl 0896.60090
[22] Zheng, Z.; Hu, G.: Generalized synchronization versus phase synchronization. Phys. rev. E 62, No. 6, 7882-7885 (2000)
[23] Taherion, S.; Lai, Y. C.: Observability of lag synchronization of coupled chaotic oscillators. Phys. rev. E 59, No. 6, R6247-R6250 (1999)
[24] Rulkov, N. F.; Sushchik, M. M.; Tsimring, L. S.; Abarbanel, H. D. I.: Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. rev. E 51, No. 2, 980-994 (1995)
[25] Kocarev, L.; Parlitz, U.: Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Phys. rev. Lett. 76, No. 11, 1816-1819 (1996)
[26] Pyragas, K.: Weak and strong synchronization of chaos. Phys. rev. E 54, No. 5, R4508-R4511 (1996)
[27] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J.: Phase synchronization of chaotic oscillators. Phys. rev. Lett. 76, No. 11, 1804-1807 (1996)
[28] Osipov, G. V.; Pikovsky, A. S.; Rosenblum, M. G.; Kurth, J.: Phase synchronization effect in a lattice of nonidentical Rössler oscillators. Phys. rev. E 55, No. 3, 2353-2361 (1997)
[29] Abarbanel, H. D. I.; Rulkov, N. F.; Sushchik, M.: Generalized synchronization of chaos: the auxiliary system approach. Phys. rev. E 53, No. 5, 4528-4535 (1996)
[30] Pecora, L. M.; Carroll, T. L.; Heagy, J. F.: Statistics for mathematical properties of maps between time series embeddings. Phys. rev. E 52, No. 4, 3420-3439 (1995)
[31] V.S. Anishchenko, T.E. Vadivasova, J. Commun. Technol. Electron. 49 (1).
[32] Pikovsky, A.; Rosenblum, M.; Osipov, G.; Kurths, J.: Phase synchronization of chaotic oscillators by external driving. Physica D 104, No. 4, 219-238 (1997) · Zbl 0898.70015
[33] Lachaux, J. P.: Studying single -- trials of the phase synchronization activity in the brain. Int. J. Bifurc. chaos 10, No. 10, 2429-2439 (2000)
[34] Quiroga, R. Q.; Kraskov, A.; Kreuz, T.; Grassberger, P.: Perfomance of different synchronization measures in real data: a case study on electroencephalographic signals. Phys. rev. E 65, 041903 (2002)
[35] Pikovsky, A. S.; Rosenblum, M. G.; Kurths, J.: Synchronization in a population of globally coupled chaotic oscillaors. Europhys. lett. 34, No. 3, 165-170 (1996)
[36] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J.: Locking -- based frequency measurement and synchronization of chaotic oscillators with complex dynamics. Phys. rev. Lett. 89, No. 26, 264102 (2002)
[37] Koronovskii, A. A.; Hramov, A. E.: Continuous wavelet analysis and its applications (In russian). (2003)
[38] Daubechies, I.: Ten lectures on wavelets. (1992) · Zbl 0776.42018
[39] Kaiser, G.: A friendly guide to wavelets. (1994) · Zbl 0839.42011
[40] Torresani, B.: Continuous wavelet transform. (1995)
[41] Grossman, A.; Morlet, J.: Decomposition of Hardy function into square integrable wavelets of constant shape. SIAM J. Math. anal. 15, No. 4, 273 (1984) · Zbl 0578.42007
[42] Torrence, C.; Compo, G. P.: A practical guide to wavelet analysis. Bull. am. Meteorol. soc. 79, No. 1, 61-78 (1998)
[43] Gusev, V. A.; Koronovskiy, A. A.; Hramov, A. E.: Application of adaptive wavelet bases to analysis of nonlinear systems with chaotic dynamics. Tech. phys. Lett. 29, No. 18, 61-69 (2003)