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Zhuravlev M. O., Koronovskii A. A., Moskalenko O. I., Hramov A. E. Intermittency near phase synchronization boundary at different time scales. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 1, pp. 109-122. DOI: 10.18500/0869-6632-2011-19-1-109-122

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Intermittency near phase synchronization boundary at different time scales

Zhuravlev Maksim Olegovich, Saratov State University
Koronovskii Aleksei Aleksandrovich, Saratov State University
Moskalenko Olga Igorevna, Saratov State University
Hramov Aleksandr Evgenevich, Innopolis University

In this paper the results of the study of the intermittent behavior taking place near the phase synchronization boundary on the different time scales of the observation are given. It has been shown that below the phase synchronization boundary, in the area of eyelet intermittency there are time scales where the ring intermittency is also observed. In other words, for the certain values of the coupling strength and time scale of observation both types of the intermittent behavior take place simultaneously. In this paper the theory of this type of the intermittent behavior is developed.

  1. Dubois M., Rubio M., and Berge P. Experimental evidence of intermittencies associated with a subharmonic bifurcation // Phys. Rev. Lett. 1983. Vol. 51. P. 1446.
  2. Boccaletti S. and Valladares D.L. Characterization of intermittent lag synchronization // Phys. Rev. E. 2000. Vol. 62, No 5. P. 7497.
  3. Boccaletti S., Kurths J., Osipov G.V., Valladares D.L., and Zhou C.S. The synchroni-zation of chaotic systems // Physics Reports. 2002. Vol. 366. P. 1.
  4. Hramov A.E. and Koronovskii A.A. Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators // Europhysics Lett. 2005. Vol. 70, No 2. P. 169.
  5. Hramov A.E., Koronovskii A.A., and Levin Yu.I. Synchronization of chaotic oscillator time scales // JETP. 2005. Vol. 127, No 4. P. 886.
  6. Berge P., Pomeau Y., and Vidal Ch. L’ordre dans le chaos. Hermann, Paris, 1988.
  7. Platt N., Spiegel E.A., and Tresser C. On-off intermittency: a mechanism for bursting // Phys. Rev. Lett. 1993. Vol. 70, No 3. P. 279.
  8. Pikovsky A.S., Osipov G.V., Rosenblum M.G., Zaks M., and Kurths J. Attractor–repeller collision and eyelet intermittency at the transition to phase synchronization // Phys. Rev. Lett. 1997. Vol. 79, No 1. P. 47.
  9. Hramov A.E., Koronovskii A.A., Kurovskaya M.K., and Boccaletti S. Ring intermittency in coupled chaotic oscillators at the boundary of phase synchronization // Phys. Rev. Lett. 2006. Vol. 97. 114101.
  10. Rosa E., Ott E., and Hess M.H. Transition to phase synchronization of chaos // Phys. Rev. Lett. 1998. Vol. 80, No 8. P. 1642.
  11. Lee K.J., Kwak Y., and Lim T.K. Phase jumps near a phase synchronization transition in systems of two coupled chaotic oscillators // Phys. Rev. Lett. 1998. Vol. 81, No 2. P. 321.
  12. Grebogi C., Ott E., and Yorke J.A. Fractal basin boundaries, long lived chaotic trancients, and unstable–unstable pair bifurcation // Phys. Rev. Lett. 1983. Vol. 50, No 13. P. 935.
  13. Короновский А.А., Куровская М.К., Москаленко О.И., Храмов А.Е. Перемежаемость типа I в присутствии шума и перемежаемость игольного ушка // Известия вузов. Прикладная нелинейная динамика. 2010. Т. 18, No 1. С. 24.
  14. Boccaletti S., Allaria E., Meucci R., and Arecchi F.T. Experimental characterization of the transition to phase synchronization of chaotic CO2 laser systems // Phys. Rev. Lett. 2002. Vol. 89, No 19. 194101.
  15. Hramov A.E. and Koronovskii A.A. An approach to chaotic synchronization // Chaos. 2004. Vol. 14, No 3. P. 603.
  16. Hramov A.E. and Koronovskii A.A. Time scale synchronization of chaotic oscillators // Physica D. 2005. Vol. 206, No 3-4. P. 252.
  17. Hramov A.E. and Koronovskii A.A. Generalized synchronization: a modified system approach // Phys. Rev. E. 2005. Vol. 71, No 6. 067201.
  18. Hramov A.E., Koronovskii A.A., and Moskalenko O.I. Generalized synchronization onset // Europhysics Letters. 2005. Vol. 72, No 6. P. 901.
  19. Журавлев М.О., Куровская М.К., Москаленко О.И. Метод выделения ламинарных и турбулентных фаз в перемежающихся временных реализациях систем, находящихся вблизи границы фазовой синхронизации // Письма в ЖТФ. 2010. Т. 36, No 10. С. 31.
  20. Hramov A.E., Koronovskii A.A., and Kurovskaya M.K. Two types of phase synchro-nization destruction // Phys. Rev. E. 2007. Vol. 75, No 3, 036205.  
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