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Koronovskii A. A., Kurovskaya 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

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Intermittency of type­-I with noise and eyelet intermittency

Koronovskii Aleksei Aleksandrovich, Saratov State University
Kurovskaya Maria Konstantinovna, Saratov State University
Moskalenko Olga Igorevna, Saratov State University
Hramov Aleksandr Evgenevich, Immanuel Kant Baltic Federal 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, Berge P. Experimental evidence of intermittencies associated with a subharmonic bifurcation. Phys. Rev. Lett. 1983;51:14461449. DOI: 10.1103/PhysRevLett.51.1446.
  2. Boccaletti S, Valladares DL. Characterization of intermittent lag synchronization. Phys. Rev. E. 2000;62(5):74977500. DOI: 10.1103/physreve.62.7497.
  3. Boccaletti S, Kurths J, Osipov GV, Valladares DL, Zhou CT. The synchronization of chaotic systems. Physics Reports. 2002;366:1101. DOI: 10.1016/S0370-1573(02)00137-0.
  4. Hramov AE, Koronovskii AA. Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators. Europhysics Lett. 2005;70(2):169175. DOI: 10.1209/epl/i2004-10488-6.
  5. Hramov AE, Koronovskii AA, Levin YuI. Synchronization of chaotic oscillator time scales. Journal of Experimental and Theoretical Physics. 2005;100(4):784794. DOI: 10.1134/1.1926439.
  6. Berge P, Pomeau Y, Vidal Ch. L’ordre dans le chaos. Paris: Hermann; 1988.
  7. Platt N, Spiegel EA, Tresser C. On–off intermittency: a mechanism for bursting. Phys. Rev. Lett. 1993;70(3):279282. DOI: 10.1103/PhysRevLett.70.279.
  8. Pikovsky AS, Osipov GV, Rosenblum MG, Zaks M, Kurths J. Attractor–repeller collision and eyelet intermittency at the transition to phase synchronization. Phys. Rev. Lett. 1997;79(1):4750. DOI: 10.1103/PhysRevLett.79.47.
  9. Pomeau Y, Manneville P. Intermittent transition to turbulence in dissipative dynamical systems. Commun. Math. Phys. 1980;74:189197. DOI: 10.1007/BF01197757.
  10. Eckmann JP, Thomas L, Wittwer P. Intermittency in the presence of noise. J. Phys. A: Math. Gen. 1981;14:31533168. DOI: 10.1088/0305-4470/14/12/013.
  11. Kye WH, Kim CM. Characteristic relations of type-I intermittency in the presence of noise. Phys. Rev. E. 2000;62(5):63046307. DOI: 10.1103/physreve.62.6304.
  12. Hramov AE, Koronovskii AA, Kurovskaya MK, Ovchinnikov AA, Boccaletti S. 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.
  13. Rosa E, Ott E, Hess MH. Transition to phase synchronization of chaos. Phys. Rev. Lett. 1998;80(8):16421645. DOI: 10.1103/PhysRevLett.80.1642.
  14. Lee KJ, Kwak Y, Lim TK. Phase jumps near a phase synchronization transition in systems of two coupled chaotic oscillators. Phys. Rev. Lett. 1998;81(2):321324. DOI: 10.1103/PhysRevLett.81.321.
  15. Grebogi C, Ott E, Yorke JA. Fractal basin boundaries, long lived chaotic transients, and unstable–unstable pair bifurcation. Phys. Rev. Lett. 1983;50(13):935938. DOI: 10.1103/PhysRevLett.50.935.
  16. Boccaletti S, Allaria E, Meucci R, 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.
  17. Pikovsky AS, Rosenblum MG, Kurths J. Phase synchronisation in regular and chaotic systems, Int. J. Bifurcation and Chaos. 2000;10(10):22912305. DOI: 10.1142/S0218127400001481.
  18. 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.
  19. Pikovsky AS, Rosenblum MG, Osipov GV, Kurths J. Phase synchronization of chaotic oscillators by external driving. Physica D. 1997;104(4):219238. DOI: 10.1016/S0167-2789(96)00301-6.
  20. Horita Takehiko, Ouchi Katsuya, Yamada T, Fujisaka H. Stochastic model of chaotic phase synchronization. II. Progress of Theoretical Physics. 2008;119(2):223235. DOI: 10.1143/PTP.119.223.
  21. Hramov AE, Koronovskii AA, Kurovskaya MK. Zero Lyapunov exponent in the vicinity of the saddle-node bifurcation point in the presence of noise. Phys. Rev. E. 2008;78:036212. DOI: 10.1103/PhysRevE.78.036212.
  22. Kurovskaya MK. Distribution of laminar phases at eyelet-type intermittency. Tech. Phys. Lett. 2008;34(12):1063–1065. DOI: 10.1134/S1063785008120225.
  23. Hramov AE, Koronovskii AA. Generalized synchronization: a modified system approach. Phys. Rev. E. 2005;71(6):067201. DOI: 10.1103/PhysRevE.71.067201.
  24. Hramov AE, Koronovskii AA, Moskalenko OI. Generalized synchronization onset. Europhysics Letters. 2005;72(6):901. DOI: 10.1209/epl/i2005-10343-4.
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