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Effect of noise on generalized synchronization of chaos: theory and experiment

  • Statistical and Nonlinear Physics
  • Regular Article
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Abstract

The influence of noise on the generalized synchronization regime in the chaotic systems with dissipative coupling is considered. If attractors of the drive and response systems have an infinitely large basin of attraction, generalized synchronization is shown to possess a great stability with respect to noise. The reasons of the revealed particularity are explained by means of the modified system approach [A.E. Hramov, A.A. Koronovskii, Phys. Rev. E 71, 067201 (2005)] and confirmed by the results of numerical calculations and experimental studies. The main results are illustrated using the examples of unidirectionally coupled chaotic oscillators and discrete maps as well as spatially extended dynamical systems. Different types of the model noise are analyzed. Possible applications of the revealed particularity are briefly discussed.

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References

  1. A.S. Pikovsky, M.G. Rosenblum, J. Kurths, Synchronization: a universal concept in nonlinear sciences (Cambridge University Press, 2001)

  2. S. Boccaletti, J. Kurths, G.V. Osipov, D.L. Valladares, C.S. Zhou, Phys. Rep. 366, 1 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  3. R. Roy, Nature 438, 298 (2005)

    Article  ADS  Google Scholar 

  4. H. Jaeger, H. Haas, Science 304, 78 (2008)

    Article  ADS  Google Scholar 

  5. U. Parlitz, L.O. Chua, L. Kocarev, K.S. Halle, A. Shang, Int. J. Bifurc. Chaos 2, 973 (1992)

    Article  MATH  Google Scholar 

  6. M.K. Cuomo, A.V. Oppenheim, S.H. Strogatz, IEEE Trans. Circuits Syst. 40, 626 (1993)

    Google Scholar 

  7. L. Kocarev, U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995)

    Article  ADS  Google Scholar 

  8. J.H. Peng, E.J. Ding, M. Ding, W. Yang, Phys. Rev. Lett. 76, 904 (1996)

    Article  ADS  Google Scholar 

  9. M.C. Eguia, M.I. Rabinovich, H.D.I. Abarbanel, Phys. Rev. E 62, 7111 (2000)

    Article  ADS  Google Scholar 

  10. I. Fischer, Y. Liu, P. Davis, Phys. Rev. A 62, 011801(R) (2000)

    Article  ADS  Google Scholar 

  11. N.F. Rulkov, M.A. Vorontsov, L. Illing, Phys. Rev. Lett. 89, 277905 (2002)

    Article  ADS  Google Scholar 

  12. Z.L. Yuan, A.J. Shields, Phys. Rev. Lett. 94, 048901 (2005)

    Article  ADS  Google Scholar 

  13. Q.S. Li, Y. Liu, Phys. Rev. E 73, 016218 (2006)

    Article  ADS  Google Scholar 

  14. A.L. Fradkov, B. Andrievsky, R.J. Evans, Phys. Rev. E 73, 066209 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  15. B. Cessac, J.A. Sepulchre, Chaos 16, 013104 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  16. G.K. Rohde, J.M. Nichols, F. Bucholtz, Chaos 18, 013114 (2008)

    Article  ADS  Google Scholar 

  17. D. Materassi, M. Basso, Int. J. Bifurc. Chaos 18, 567 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  18. A.A. Koronovskii, O.I. Moskalenko, A.E. Hramov, Phys. Uspekhi 52, 1213 (2009)

    Article  ADS  Google Scholar 

  19. S.H. Strogatz, Nonlinear dynamics and chaos, with applications to physics, biology, chemistry, and engineering (Addison-Wesley, New York, 1994)

  20. R.C. Elson et al., Phys. Rev. Lett. 81, 5692 (1998)

    Article  ADS  Google Scholar 

  21. R. Porcher, G. Thomas, Phys. Rev. E 64, 010902(R) (2001)

    Article  ADS  Google Scholar 

  22. L. Glass, Nature (London) 410, 277 (2001)

    Article  ADS  Google Scholar 

  23. A.N. Pavlov, O.V. Sosnovtseva, A.R. Ziganshin, N.H. Holstein-Rathlou, E. Mosekilde, Physica A 316, 233 (2002)

    Article  ADS  MATH  Google Scholar 

  24. M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Fluc. Noise Lett. 4, L53 (2004)

    Article  Google Scholar 

  25. W.L. Ditto, S.N. Rauseo, M.L. Spano, Phys. Rev. Lett. 65, 3211 (1990)

    Article  ADS  Google Scholar 

  26. C.M. Ticos, E. Rosa, W.B. Pardo, J.A. Walkenstein, M. Monti, Phys. Rev. Lett. 85, 2929 (2000)

    Article  ADS  Google Scholar 

  27. E. Rosa, W.B. Pardo, C.M. Ticos, J.A. Walkenstein, M. Monti, Int. J. Bifurc. Chaos 10, 2551 (2000)

    MATH  Google Scholar 

  28. A.E. Hramov, A.A. Koronovskii, P.V. Popov, I.S. Rempen, Chaos 15, 013705 (2005)

    Article  ADS  Google Scholar 

  29. B.S. Dmitriev, A.E. Hramov, A.A. Koronovskii, A.V. Starodubov, D.I. Trubetskov, Y.D. Zharkov, Phys. Rev. Lett. 102, 074101 (2009)

    Article  ADS  Google Scholar 

  30. M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 76, 1804 (1996)

    Article  ADS  Google Scholar 

  31. N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, H.D.I. Abarbanel, Phys. Rev. E 51, 980 (1995)

    Article  ADS  Google Scholar 

  32. L. Kocarev, U. Parlitz, Phys. Rev. Lett. 76, 1816 (1996)

    Article  ADS  Google Scholar 

  33. M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 4193 (1997)

    Article  ADS  Google Scholar 

  34. S. Taherion, Y.C. Lai, Phys. Rev. E 59, R6247 (1999)

    Article  ADS  Google Scholar 

  35. L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  36. L.M. Pecora, T.L. Carroll, Phys. Rev. A 44, 2374 (1991)

    Article  ADS  Google Scholar 

  37. A.E. Hramov, A.A. Koronovskii, Chaos 14, 603 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  38. A.E. Hramov, A.A. Koronovskii, Physica D 206, 252 (2005)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  39. E. Stone, P. Holmes, SIAM J. Appl. Math. 50, 726 (1990)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  40. Y. Kifer, Israel J. Math 40, 74 (1981)

    Article  MathSciNet  Google Scholar 

  41. M.K. Ali, Phys. Rev. E 55, 4804 (1997)

    Article  ADS  Google Scholar 

  42. R. Toral, C.R. Mirasso, E. Hernández-Garsia, O. Piro, Chaos 11, 665 (2001)

    Article  ADS  MATH  Google Scholar 

  43. V.S. Anishchenko, T.E. Vadivasova, J. Commun. Technol. Electron. 47, 117 (2002)

    Google Scholar 

  44. C.S. Zhou, J. Kurths, Phys. Rev. Lett. 88, 230602 (2002)

    Article  ADS  Google Scholar 

  45. C.S. Zhou, J. Kurths, I.Z. Kiss, J.L. Hudson, Phys. Rev. Lett. 89, 014101 (2002)

    Article  ADS  Google Scholar 

  46. S.Y. Kim, W. Lim, A. Jalnine, S.P. Kuznetsov, Phys. Rev. E 67, 016217 (2003)

    Article  ADS  Google Scholar 

  47. C.S. Zhou, J. Kurths, E. Allaria, S. Boccaletti, R. Meucci, F.T. Arecchi, Phys. Rev. E 67, 015205(R) (2003)

    ADS  Google Scholar 

  48. D.S. Goldobin, A.S. Pikovsky, Phys. Rev. E 71, 045201(R) (2005)

    Article  ADS  MathSciNet  Google Scholar 

  49. A.E. Hramov, A.A. Koronovskii, O.I. Moskalenko, Phys. Lett. A 354, 423 (2006)

    Article  ADS  Google Scholar 

  50. S. Guan, Y.C. Lai, C.H. Lai, Phys. Rev. E 73, 046210 (2006)

    Article  ADS  Google Scholar 

  51. J.F. Heagy, T.L. Carroll, L.M. Pecora, Phys. Rev. E 52, R1253 (1995)

    Article  ADS  Google Scholar 

  52. D.J. Gauthier, J.C. Bienfang, Phys. Rev. Lett. 77, 1751 (1996)

    Article  ADS  Google Scholar 

  53. S. Fahy, D.R. Hamann, Phys. Rev. Lett. 69, 761 (1992)

    Article  ADS  Google Scholar 

  54. A. Maritan, J.R. Banavar, Phys. Rev. Lett. 72, 1451 (1994)

    Article  ADS  Google Scholar 

  55. R.V. Jensen, Phys. Rev. E 58, R6907 (1998)

    Article  ADS  Google Scholar 

  56. L. Zhu, A. Raghu, Y.C. Lai, Phys. Rev. Lett. 86, 4017 (2001)

    Article  ADS  Google Scholar 

  57. A.E. Hramov, A.A. Koronovskii, M.K. Kurovskaya, A.A. Ovchinnikov, S. Boccaletti, Phys. Rev. E 76, 026206 (2007)

    Article  ADS  Google Scholar 

  58. A.E. Hramov, A.A. Koronovskii, M.K. Kurovskaya, Phys. Rev. E 78, 036212 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  59. C. Grebogi, E. Ott, J.A. Yorke, Phys. Rev. Lett. 48, 1507 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  60. O.I. Moskalenko, A.A. Koronovskii, A.E. Hramov, Phys. Lett. A 374, 2925 (2010)

    Article  ADS  Google Scholar 

  61. A.E. Hramov, A.A. Koronovskii, V.I. Ponomarenko, M.D. Prokhorov, Phys. Rev. E 73, 026208 (2006)

    Article  ADS  Google Scholar 

  62. A.E. Hramov, A.A. Koronovskii, V.I. Ponomarenko, M.D. Prokhorov, Phys. Rev. E 75, 056207 (2007)

    Article  ADS  Google Scholar 

  63. K. Pyragas, Phys. Rev. E 54, R4508 (1996)

    Article  ADS  Google Scholar 

  64. H.D.I. Abarbanel, N.F. Rulkov, M.M. Sushchik, Phys. Rev. E 53, 4528 (1996)

    Article  ADS  Google Scholar 

  65. A.A. Koronovskii, A.E. Hramov, A.E. Khramova, JETP Lett. 82, 160 (2005)

    Article  ADS  Google Scholar 

  66. A.E. Hramov, A.A. Koronovskii, Phys. Rev. E 71, 067201 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  67. A.E. Hramov, A.A. Koronovskii, O.I. Moskalenko, Europhys. Lett. 72, 901 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  68. A. Koronovskii, A.V. Starodubov, A.E. Khramova, Tech. Phys. Lett. 32, 864 (2006)

    Article  ADS  Google Scholar 

  69. B. Sklar, Digital communication. Fundamentals and application (Prentice Hall PTR, New Jersey, 2001)

  70. H.G. Schuster, Deterministic Chaos (Physik-Verlag, Weinheim, 1984)

  71. C. Grebogi, E. Ott, J.A. Yorke, Phys. Rev. Lett. 50, 935 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  72. N.N. Nikitin, S.V. Pervachev, V.D. Razevig, Automation and telemechanics 4, 133 (2008), in Russian

    Google Scholar 

  73. E. Ott, J.C. Sommerer, Phys. Lett. A 188, 39 (1994)

    Article  ADS  Google Scholar 

  74. A.E. Hramov, A.A. Koronovskii, P.V. Popov, Phys. Rev. E 72, 037201 (2005)

    Article  ADS  Google Scholar 

  75. J. García-Ojalvo, J.M. Sancho, Noise in Spatially Extended Systems (Springer, New York, 1999)

  76. A.E. Hramov, A.A. Koronovskii, P.V. Popov, Phys. Rev. E 77, 036215 (2008)

    Article  ADS  Google Scholar 

  77. N.F. Rulkov, Chaos 6, 262 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  78. A. Uchida, R. McAllister, R. Meucci, R. Roy, Phys. Rev. Lett. 91, 174101 (2003)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaya, 83, 410012, Saratov, Russia

    O. I. Moskalenko, A. E. Hramov, A. A. Koronovskii & A. A. Ovchinnikov

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  1. O. I. Moskalenko
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  2. A. E. Hramov
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  3. A. A. Koronovskii
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  4. A. A. Ovchinnikov
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Correspondence to O. I. Moskalenko.

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Moskalenko, O.I., Hramov, A.E., Koronovskii, A.A. et al. Effect of noise on generalized synchronization of chaos: theory and experiment. Eur. Phys. J. B 82, 69–82 (2011). https://doi.org/10.1140/epjb/e2011-11019-1

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