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

For citation:

Koronovskii A. A., Kurovskaja M. K., Moskalenko O. I., Hramov A. E. Intermittency of type­-I with noise and eyelet intermittency. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 1, pp. 24-36. DOI: 10.18500/0869-6632-2010-18-1-24-36

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 55)
Article type: 

Intermittency of type­-I with noise and eyelet intermittency

Koronovskii Aleksei Aleksandrovich, Saratov State University
Kurovskaja Marija Konstantinovna, Saratov State University
Moskalenko Olga Igorevna, Saratov State University
Hramov Aleksandr Evgenevich, Innopolis University

In this article we compare the characteristics of two types of the intermittent behavior (type-I intermittency in the presence of noise and eyelet intermittency) supposed hitherto to be the different phenomena. We prove that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is proven by the consideration of different sample systems, such as quadratic map, van der Pol oscillator and Rossler system.

  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.T. The synchronization 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. Pomeau Y. and Manneville P. Intermittent transition to turbulence in dissipative dynamical systems // Commun. Math. Phys. 1980. Vol. 74. P. 189.
  10. Eckmann J.P., Thomas L., and Wittwer P. Intermittency in the presence of noise // J. Phys. A: Math. Gen. 1981. Vol. 14. P. 3153.
  11. Kye W.-H. and Kim C.-M. Characteristic relations of type-I intermittency in the presence of noise // Phys. Rev. E. 2000. Vol. 62, No 5. P. 6304.
  12. Hramov A.E., Koronovskii A.A., Kurovskaya M.K., Ovchinnikov A.A., and Boccaletti S. Length distribution of laminar phases for type-I intermittency in the presence of noise // Phys. Rev. E. 2007. Vol. 76, No 2. 026206.
  13. Rosa E., Ott E., and Hess M.H. Transition to phase synchronization of chaos // Phys. Rev. Lett. 1998. Vol. 80, No 8. P. 1642.
  14. 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.
  15. 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.
  16. 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.
  17. Pikovsky A.S., Rosenblum M.G., and Kurths J. Phase synchronisation in regular and chaotic systems, Int. J. Bifurcation and Chaos. 2000. Vol. 10, No 10. P. 2291.
  18. Hramov A.E., Koronovskii A.A., and Kurovskaya M.K. Two types of phase synchronization destruction // Phys. Rev. E. 2007. Vol. 75, No 3, 036205.
  19. Pikovsky A.S., Rosenblum M.G., Osipov G.V., and Kurths J. Phase synchronization of chaotic oscillators by external driving // Physica D. 1997. Vol. 104, No 4. P. 219.
  20. Horita Takehiko, Ouchi Katsuya, Yamada T., and Fujisaka H. Stochastic model of chaotic phase synchronization. II// Progress of Theoretical Physics. 2008. Vol. 119, No 2. P. 223.
  21. Hramov A.E., Koronovskii A.A., and Kurovskaya M.K. Zero Lyapunov exponent in the vicinity of the saddle-node bifurcation point in the presence of noise // Phys. Rev. E. 2008. Vol. 78, 036212.
  22. Куровская М.К. Распределение длительности ламинарных фаз при перемежаемости «игольного ушка» // Письма в ЖТФ. 2008. Т. 34, No 12. С. 483.
  23. Hramov A.E. and Koronovskii A.A. Generalized synchronization: a modified system approach // Phys. Rev. E. 2005. Vol. 71, No 6, 067201.
  24. Hramov A.E., Koronovskii A.A., and Moskalenko O.I. Generalized synchronization onset // Europhysics Letters. 2005. Vol. 72, No 6. P. 901.
Short text (in English):
(downloads: 40)