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Koronovskii A. A., Moskalenko O. I., Hramov A. E. Effect of noise on generalized synchronization of spatially extended systems described by Ginzburg–Landau equations. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 4, pp. 3-11. DOI: 10.18500/0869-6632-2011-19-4-3-11

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Effect of noise on generalized synchronization of spatially extended systems described by Ginzburg–Landau equations

Koronovskii Aleksei Aleksandrovich, Saratov State University
Moskalenko Olga Igorevna, Saratov State University
Hramov Aleksandr Evgenevich, Immanuel Kant Baltic Federal University

Effect of noise on generalized synchronization in spatially extended systems described by Ginzburg–Landau equations being in the spatio-temporal chaotic regime is studied. It is shown, that noise does not affect the synchronous regime threshold in such systems. The reasons of the revealed particularity have been explained by means of the modified system approach and confirmed by the results of numerical simulation. 



  1. Boccaletti S, Kurths J, Osipov GV, Valladares DL, and Zhou CS. The synchronization of chaotic systems. Physics Reports. 2002;366(1–2):1–101. DOI: 10.1016/S0370-1573(02)00137-0.
  2. Glass L. Synchronization and rhythmic processes in physiology. Nature (London). 2001;410(6825):277–284. DOI: 10.1038/35065745.
  3. Prokhorov MD, Ponomarenko VI, Gridnev VI, Bodrov MB, and Bespyatov AB. Synchronization between main rhythmic processes in the human cardiovascular system. Phys. Rev. E. 2003;68(4):041913. DOI: 10.1103/PhysRevE.68.041913.
  4. Sosnovtseva OV, Pavlov AN, Mosekilde E, Yip KP, Holstein-Rathlou NH, and Marsh DJ. Synchronization among mechanisms of renal autoregulation is reduced in hypertensive rats. American Journal of Physiology (Renal Physiology). 2007;293(5):F1545–F1555. DOI: 10.1152/ajprenal.00054.2007.
  5. Koronovskii AA, Moskalenko OI, Hramov AE. On the use of chaotic synchronization for secure communication. Phys. Usp. 2009;52(12):1213–1238. DOI: 10.3367/UFNe.0179.200912c.1281.
  6. Heagy JF, Carroll TL, and Pecora LM. Desynchronization by periodic orbits. Phys. Rev. E. 1995;52(2):R1253–R1256. DOI: 10.1103/PhysRevE.52.R1253.
  7. Gauthier DJ and Bienfang JC. Intermittent loss of synchronization in coupled chaotic oscillators: Toward a new criterion for high-quality synchronization. Phys. Rev. Lett. 1996;77(9):1751–1754. DOI: 10.1103/physrevlett.77.1751.
  8. Zhu L, Raghu A, and Lai YC. Experimental observation of superpersistent chaotic transients. Phys. Rev. Lett. 2001;86(18):4017–4020. DOI: 10.1103/PhysRevLett.86.4017.
  9. Zhou CS, Kurths J, Kiss IZ, and Hudson JL. Noise-enhanced phase synchronization of chaotic oscillators. Phys. Rev. Lett. 2002;89(1):014101. DOI: 10.1103/PhysRevLett.89.014101.
  10. Kim SY, Lim W, Jalnine A, and Kuznetsov SP. Characterization of the noise effect on weak synchronization. Phys. Rev. E. 2003;67(1):016217. DOI: 10.1103/PhysRevE.67.016217.
  11. Zhou CS, Kurths J, Allaria E, Boccaletti S, Meucci R, and Arecchi FT. Noise–enhanced synchronization of homoclinic chaos in a CO2 laser. Phys. Rev. E. 2003;67(1):015205. DOI: 10.1103/physreve.67.015205.
  12. Goldobin DS and Pikovsky AS. Synchronization and desynchronization of self-sustained oscillators by common noise. Phys. Rev. E. 2005;71(4):045201. DOI: 10.1103/PhysRevE.71.045201.
  13. Guan S, Lai YC, and Lai CH. Effect of noise on generalized chaotic synchronization. Phys. Rev. E. 2006;73(4):046210. DOI: 10.1103/PhysRevE.73.046210.
  14. Moskalenko OI, Ovchinnikov AA. Investigation of the noise influence on generalized chaotic synchronization in dissipatively coupled dynamic systems: Synchronous regime stability in the presence of external noise and possible practical applications. J. Commun. Technol. Electron. 2010;55(4):407–419. DOI: 10.1134/S1064226910040066.
  15. Maritan A and Banavar JR. Chaos, noise and synchronization. Phys. Rev. Lett. 1994;72(10):1451–1454. DOI: 10.1103/PhysRevLett.72.1451.
  16. Toral R, Mirasso CR, Hernandez-Garsia E, and Piro O. Analytical and numerical studies of noise–induced synchronization of chaotic systems. Chaos. 2001;11(3):665–673. DOI: 10.1063/1.1386397.
  17. Popov PV, Filatov RA, Koronovskii AA, Hramov AE. Spatiotemporal chaos synchronization in beam-plasma systems with supercritical current. Tech. Phys. Lett. 2005;31(3):221–224. DOI: 10.1134/1.1894438.
  18. Koronovskii AA, Popov PV, Hramov AE. Generalized chaotic synchronization in coupled Ginzburg-Landau equations. J. Exp. Theor. Phys. 2006;103(4):654–665. DOI: 10.1134/S1063776106100189.
  19. Rulkov NF, Sushchik MM, Tsimring LS, and Abarbanel HDI. Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E. 1995;51(2):980–994. DOI: 10.1103/PhysRevE.51.980.
  20. Pyragas K. Conditional Lyapunov exponents from time series. Phys. Rev. E. 1997;56(5):5183–5188. DOI: 10.1103/PhysRevE.56.5183.
  21. Koronovskii AA, Moskalenko OI, Frolov NS, Hramov AE. On the spectrum of spatial Lyapunov exponents for a nonlinear active medium described by a complex Ginzburg-Landau equation. Tech. Phys. Lett. 2010;36(7):645–647. DOI: 10.1134/S1063785010070187.
  22. Abarbanel HDI, Rulkov NF, and Sushchik MM. Generalized synchronization of chaos: The auxiliary system approach. Phys. Rev. E. 1996;53(5):4528–4535. DOI: 10.1103/PhysRevE.53.4528.
  23. Hramov AE, Koronovskii AA, and Popov PV. Generalized synchronization in coupled Ginzburg–Landau equations and mechanisms of its arising. Phys. Rev. E. 2005;72(3):037201. DOI: 10.1103/PhysRevE.72.037201.
  24. Garcia-Ojalvo J and Sancho J.M. Noise in Spatially Extended Systems. New York: Springer; 1999. 307 p. DOI: 10.1007/978-1-4612-1536-3.
  25. Hramov AE, Koronovskii AA. Generalized synchronization: A modified system approach. Phys. Rev. E. 2005;71(6):067201. DOI: 10.1103/PhysRevE.71.067201.
  26. Koronovskii AA, Popov PV, Hramov AE. Generalized synchronization in autooscillatory media. Tech. Phys. Lett. 2005;31(11):951–954. DOI: 10.1134/1.2136962.
  27. Hramov AE, Koronovskii AA, and Popov PV. Incomplete noise-induced synchronization of spatially extended systems. Phys. Rev. E. 2008;77(2):036215. DOI: 10.1103/PhysRevE.77.036215.
  28. Koronovskii AA, Popov PV, Hramov AE. Noise-induced synchronization of spatiotemporal chaos in the Ginzburg-Landau equation. J. Exp. Theor. Phys. 2008;107(5):899–907. DOI: 10.1134/S1063776108110228.
  29. Hramov AE, Koronovskii AA, and Moskalenko OI. Are generalized synchronization and noise-induced synchronization identical types of synchronous behavior of chaotic oscillators? Phys. Lett. A. 2006;354(5–6):423–427. DOI: 10.1016/j.physleta.2006.01.079.  
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