ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

Zhuravlev M. O., Koronovskii A. A., Moskalenko O. I., Hramov A. E. Ring intermittency near the boundary of time scale synchronization. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 4, pp. 12-24. DOI: 10.18500/0869-6632-2011-19-4-12-24

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 180)
Language: 
Russian
Article type: 
Article
UDC: 
517.9

Ring intermittency near the boundary of time scale synchronization

Autors: 
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
Abstract: 

In this paper the intermittent behavior taking place near the boundary of the synchronous time scales of interacted chaotic oscillators being in the synchronous regime is studied. At the regime of time-scale synchronization the system demonstrates synchronous dynamics in a certain range of the time scales whereas the processes on the other time scales remain asynchronous. On the basis of analysis of statistical characteristics of the intermittent behavior, i.e. the laminar phase length distributions and dependence of the mean length of the laminar phases on the criticality parameter, the revealed type of the intermittent behavior is shown to be the ring intermittency.

Reference: 
  1. Berge P, Pomeau Y, Vidal K. Order Within Chaos. New York: Wiley; 1984. 329 p.
  2. Manneville P, Pomeau Y. Different ways to turbulence in dissipative dynamical systems. Physica D. 1980;1(2):219–226. DOI: 10.1016/0167-2789(80)90013-5.
  3. Berge P, Pomeau Y, Vidal C. L’Ordre Dans Le Chaos. Hermann, Paris; 1988. 353 p.
  4. Dubois M, Rubio M, 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.
  5. Platt N, Spiegel EA, Tresser C. On–off intermittency: A mechanism for bursting. Phys. Rev. Lett. 1993;70(3):279–282. DOI: 10.1103/PhysRevLett.70.279.
  6. Heagy JF, Platt N, Hammel SM. Characterization of on–off intermittency. Phys. Rev. E. 1994;49(2):1140–1150. DOI: 10.1103/PhysRevE.49.1140.
  7. Lai YC. Symmetry-breaking bifurcation with on-off intermittency in chaotic dynamical systems. Phys. Rev. E. 1996;53(5):R4267–R4270. DOI: 10.1103/PhysRevE.53.R4267.
  8. Pikovsky AS, Osipov GV, Rosenblum MG et al. 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, 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. Rosenblum MG, Pikovsky AS, Kurths J. From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 1997;78(22):4193–4196. DOI: 10.1103/PhysRevLett.78.4193.
  11. Porcher R, Thomas G. Estimating Lyapunov exponents in biomedical time series. Phys. Rev. E. 2001;64(1):010902. DOI: 10.1103/PhysRevE.64.010902.
  12. Hramov AE, Koronovskii AA. Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators. Europhys. Lett. 2005;70(2):169–175. DOI: 10.1209/epl/i2004-10488-6.
  13. Boccaletti S, Valladares DL. Characterization of intermittent lag synchronization. Phys. Rev. E. 2000;62(5):7497–7500. DOI: 10.1103/physreve.62.7497.
  14. Rosenblum MG, Pikovsky AS, Kurths J. Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 1996;76(11):1804–1807. DOI: 10.1103/physrevlett.76.1804.
  15. Rulkov NF, Sushchik MM, Tsimring LS, Abarbanel HD. Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E. 1995;51(2):980–994. DOI: 10.1103/PhysRevE.51.980.
  16. Hramov AE, Koronovskii AA. Generalized synchronization: a modified system approach. Phys. Rev. E. 2005;71(6):067201. DOI: 10.1103/PhysRevE.71.067201.
  17. Pecora LM, Carroll TL. Synchronization in chaotic systems. Phys. Rev. Lett. 1990;64(8):821–824. DOI: 10.1103/PhysRevLett.64.821.
  18. Hramov AE, Koronovskii AA. An approach to chaotic synchronization. Chaos. 2004;14(3):603–610. DOI: 10.1063/1.1775991.
  19. Hramov AE, Koronovskii AA. Time scale synchronization of chaotic oscillators. Physica D. 2005;206(3–4):252–264. DOI: 10.1016/j.physd.2005.05.008.
  20. Rosenblum MG, Pikovsky AS, Kurths J. Locking–based frequency measurement and synchronization of chaotic oscillators with complex dynamics. Phys. Rev. Lett. 2002;89(26):264102. DOI: 10.1103/PhysRevLett.89.264102.
  21. Koronovskii AA, Moskalenko OI, Hramov AE. New universality type in chaotic synchronization of dynamic systems. Jetp Lett. 2004;80(1):20–22. DOI: 10.1134/1.1800207.
  22. Hramov AE, Koronovskii AA, Kurovskaya MK et al. Length distribution of laminar phases for type-I intermittency in the presence of noise. Phys. Rev. E. 2007;76(2):026206. DOI: 10.1103/PhysRevE.76.026206.
  23. Hramov AE, Koronovskii AA, Kurovskaya MK. Two types of phase synchronization destruction. Phys. Rev. E. 2007;75(3):036205. DOI: 10.1103/PhysRevE.75.036205.
  24. 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. 
Received: 
12.11.2010
Accepted: 
23.06.2011
Published: 
30.09.2011
Short text (in English):
(downloads: 91)