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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, Immanuel Kant Baltic Federal 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;51(16):1446–1449. DOI: 10.1103/PhysRevLett.51.1446.
  2. Boccaletti S, and Valladares DL. Characterization of intermittent lag synchronization. Phys. Rev. E. 2000;62(5):7497–7500. DOI: 10.1103/physreve.62.7497.
  3. 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.
  4. Hramov AE, and Koronovskii AA. Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators. Europhysics Lett. 2005;70(2):169–175. DOI: 10.1209/epl/i2004-10488-6.
  5. Hramov AE, Koronovskii AA, and Levin YI. Synchronization of chaotic oscillator time scales. JETP. 2005;100(4):784–794. DOI: 10.1134/1.1926439.
  6. Berge P, Pomeau Y, and Vidal C. L’ordre Dans Le Chaos. Hermann, Paris; 1988. 353 p.
  7. Platt N, Spiegel EA, and Tresser C. On-off intermittency: a mechanism for bursting. Phys. Rev. Lett. 1993;70(3):279–282. DOI: 10.1103/PhysRevLett.70.279.
  8. Pikovsky AS, Osipov GV, Rosenblum MG, Zaks M, and Kurths J. Attractor–repeller collision and eyelet intermittency at the transition to phase synchronization. Phys. Rev. Lett. 1997;79(1):47–50. DOI: 10.1103/PhysRevLett.79.47.
  9. Hramov AE, Koronovskii AA, Kurovskaya MK, and Boccaletti S. Ring intermittency in coupled chaotic oscillators at the boundary of phase synchronization. Phys. Rev. Lett. 2006;97(11):114101. DOI: 10.1103/PhysRevLett.97.114101.
  10. Rosa E, Ott E, and Hess MH. Transition to phase synchronization of chaos. Phys. Rev. Lett. 1998;80(8):1642–1645. DOI: 10.1103/PhysRevLett.80.1642.
  11. Lee KJ, Kwak Y, and Lim TK. Phase jumps near a phase synchronization transition in systems of two coupled chaotic oscillators. Phys. Rev. Lett. 1998;81(2):321–324. DOI: 10.1103/PhysRevLett.81.321.
  12. Grebogi C, Ott E, and Yorke JA. Fractal basin boundaries, long lived chaotic transients, and unstable–unstable pair bifurcation. Phys. Rev. Lett. 1983;50(13):935–938. DOI: 10.1103/PhysRevLett.50.935.
  13. Koronovskii AA, Kurovskaja MK, Moskalenko OI, Hramov AE. Intermittency of type­-I with noise and eyelet intermittency. Izvestiya VUZ. Applied Nonlinear Dynamics. 2010;18(1):24–36 (in Russian). DOI: 10.18500/0869-6632-2010-18-1-24-36.
  14. Boccaletti S, Allaria E, Meucci R, and Arecchi FT. Experimental characterization of the transition to phase synchronization of chaotic CO2 laser systems. Phys. Rev. Lett. 2002;89(19):194101. DOI: 10.1103/physrevlett.89.194101.
  15. Hramov AE, and Koronovskii AA. An approach to chaotic synchronization. Chaos. 2004;14(3):603–610. DOI: 10.1063/1.1775991.
  16. Hramov AE, and Koronovskii AA. Time scale synchronization of chaotic oscillators. Physica D. 2005;206(3–4):252–264. DOI: 10.1016/j.physd.2005.05.008.
  17. Hramov AE, and Koronovskii AA. Generalized synchronization: A modified system approach. Phys. Rev. E. 2005;71(6):067201. DOI: 10.1103/PhysRevE.71.067201.
  18. Hramov AE, Koronovskii AA, and Moskalenko OI. Generalized synchronization onset. Europhysics Letters. 2005;72(6):901–907. DOI: 10.1209/epl/i2005-10343-4.
  19. Zhuravlev MO, Kurovskaya MK, Moskalenko OI. Method for separating laminar and turbulent intervals in intermittent time series of systems near the phase synchronization boundary. Tech. Phys. Lett. 2010;36(5):457–460. DOI: 10.1134/S1063785010050202.
  20. Hramov AE, Koronovskii AA, and Kurovskaya MK. Two types of phase synchronization destruction. Phys. Rev. E. 2007;75(3):036205. DOI: 10.1103/PhysRevE.75.036205.
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