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Partial spatial synchronization of chaotic oscillations in the Ginzburg-Landau equation

  • Solitons and Chaos
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Abstract

A possibility of generalized synchronization between two parts of a spatially distributed system being in space-time chaos is demonstrated with the Ginzburg-Landau equation used as an example. Regions of the distributed system parameters at which the functional relationship is established between the parts of the system are determined.

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References

  1. A. S. Pikovsky, M. G. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge Univ. Press, Cambridge, 2001).

    Book  MATH  Google Scholar 

  2. A. S. Dmitriev and A. I. Panas, Dynamic Chaos: New Information Carriers for Communication Systems (Fizmatlit, Moscow, 2002) [in Russian].

    Google Scholar 

  3. B. S. Dmitriev, A. E. Hramov, A. A. Koronovskii, A. V. Starodubov, D. I. Trubetskov, and Y. D. Zharkov, “First Experimental Observation of Generalized Synchronization Phenomena in Microwave Oscillators,” Phys. Rev. Lett. 102, 074101 (2009).

    Article  ADS  Google Scholar 

  4. M. D. Prokhorov, V. I. Ponomarenko, V. I. Gridnev, M. B. Bodrov, and A. B. Bespyatov, “Synchronization between Main Rhytmic Processes in the Human Cardiovascular System,” Phys. Rev. E. 68, 041913 (2003).

    Article  ADS  Google Scholar 

  5. P. A. Tass, T. Fieseler, J. Dammers, K. T. Dolan, P. Morosan, M. Majtanik, F. Boers, A. Muren, K. Zilles, and G.R. Fink, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).

    Article  ADS  Google Scholar 

  6. A. A. Koronovskii, O. I. Moskalenko, and A. E. Hramov, “On the Use of Chaotic Synchronization for Secure Communication,” Phys.-Usp. 52(12), 1213 (2009).

    Article  ADS  Google Scholar 

  7. N. F. Rulkov, M.M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel, “Generalized Synchronization of Chaos in Directionally Coupled Chaotic Systems,” Phys. Rev. E. 51, 980 (1995).

    Article  ADS  Google Scholar 

  8. K. Pyragas, “Weak and Strong Synchronization of Chaos,” Phys. Rev. E. 54, R4508 (1996).

    Article  ADS  Google Scholar 

  9. A. E. Hramov, A.A. Koronovskii, and P.V. Popov, “Generalized Synchronization in Coupled Ginzburg-Landau Equations and Mechanisms of Its Arising,” Phys. Rev. E. 72, 037201 (2005).

    Article  ADS  Google Scholar 

  10. A. A. Koronovskii, P.V. Popov, and A.E. Hramov, “Generalized Chaotic Synchronization in Coupled Ginzburg-Landau Equations,” JETP. 103(4), 654 (2006).

    Article  ADS  Google Scholar 

  11. R. A. Filatov, A. E. Hramov, and A. A. Koronovskii, “Chaotic Synchronization in Coupled Spatially Extended Beam-Plasma Systems,” Phys. Lett. A. 358, 301 (2006).

    Article  ADS  MATH  Google Scholar 

  12. R. A. Filatov, P.V. Popov, A. A. Koronovskii, and A. E. Hramov, “Spatiotemporal Chaos Synchronization in Beam-Plasma Systems with Sypercritical Current,” Tech. Phys. Lett. 31(3), 221 (2005).

    Article  Google Scholar 

  13. I. S. Aranson and L. Kramer, “TheWorld of theComplex Ginzburg-Landau Equation,” Rev. Mod. Phys. 74, 99 (2002).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, “Generalized Synchronization of Chaos: The Auxiliary System Approach,” Phys. Rev. E. 53, 4528 (1996).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia

    A. A. Koronovskii, N. S. Frolov & A. E. Hramov

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  1. A. A. Koronovskii
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  2. N. S. Frolov
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  3. A. E. Hramov
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Correspondence to A. E. Hramov.

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Koronovskii, A.A., Frolov, N.S. & Hramov, A.E. Partial spatial synchronization of chaotic oscillations in the Ginzburg-Landau equation. Phys. Wave Phen. 19, 155–158 (2011). https://doi.org/10.3103/S1541308X11020129

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  • DOI: https://doi.org/10.3103/S1541308X11020129

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