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Koronovskii A. A., Kurovskaya M. K., Hramov A. E. Distribution of the laminar phases in the case of type-I intermittency with noise. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 5, pp. 43-59. DOI: 10.18500/0869-6632-2009-17-5-43-59

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Distribution of the laminar phases in the case of type-I intermittency with noise

Koronovskii Aleksei Aleksandrovich, Saratov State University
Kurovskaya Maria Konstantinovna, Saratov State University
Hramov Aleksandr Evgenevich, Immanuel Kant Baltic Federal University

This work is devoted to the intermittent behavior caused by the interplay between the dynamical mechanisms resulting in the type­I intermittency and the stochastic processes. The analytical consideration of the laminar phase distribution is given.

  1. Berge P, Pomeau Y, Vidal Ch. L’ordre dans le chaos. Paris: Hermann; 1988. 353 p.
  2. Dubois M, Rubio M, Berge P. Experimental evidence of intermiasttencies associated with a subharmonic bifurcation. Phys. Rev. Lett. 1983;51(16):1446–1449. DOI: 10.1103/PhysRevLett.51.1446.
  3. 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.
  4. 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.
  5. Boccaletti S, Valladares DL. Characterization of intermittent lag synchronization. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000;62(5):7497–7500. DOI: 10.1103/physreve.62.7497.
  6. Hramov AE, Koronovskii AA. Intermittent generalized synchronization in unidi-rectionally coupled chaotic oscillators. Europhysics Lett. 2005;70(2):169–175. DOI: 10.1209/epl/i2004-10488-6.
  7. 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):47–50. DOI: 10.1103/PhysRevLett.79.47.
  8. 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):321–324. DOI: 10.1063/1.59935.
  9. 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.
  10. 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.
  11. Neiman A, Silchenko A, Anishchenko VS, Schimansky-Geier L. Stochastic resonance: Noise-enhanced phase coherence. Phys. Rev. E. 1998;58(6):7118–7125.
  12. Anishchenko VS, Kopeikin AS, Vadivasova TE, Strelkova GI, Kurths J. Influence of noise on statistical properties of nonhyperbolic attractors. Phys. Rev. E. 2000;62(6):7886–7893. DOI: 10.1103/PHYSREVE.62.7886.
  13. Sosnovtseva OV, Fomin AI, Postnov DE, Anishchenko VS. Clustering of noise-induced oscillations. Phys. Rev. E. 2001;64(2):026204. DOI: 10.1103/PhysRevE.64.026204.
  14. Pikovsky AS, Kurths J. Coherence resonance in a noise-driven excitable system. Phys. Rev. Lett. 1997;78(5):775–778. DOI: 10.1103/PhysRevLett.78.775.
  15. Mangioni S, Deza R, Wio H, Toral R. Disordering effects of color in nonequilibrium phase transitions induced by multiplicative noise. Phys. Rev. Lett. 1997;79(13):2389–2393. DOI: 10.1103/PhysRevLett.79.2389.
  16. Zaikin AA, Kurths J, Schimansky-Geier L. Doubly stochastic resonance. Phys. Rev. Lett. 2000;85(2):227–231. DOI: 10.1103/PhysRevLett.85.227.
  17. Neiman A, Russell David F. Synchronization of noise-induced bursts in noncoupled sensory neurons. Phys. Rev. Lett. 2002;88(13):138103. DOI: 10.1103/PhysRevLett.88.138103.
  18. Zhou CT, Kurths J, Kiss IZ, Hudson JL. Noise-enhanced phase synchronization of chaotic oscillators. Phys. Rev. Lett. 2002;89(1):014101. DOI: 10.1103/PhysRevLett.89.014101.
  19. Zhou CT, Kurths J, Allaria E, Boccaletti S, Meucci R, Arecchi FT. Noiseenhanced synchronization of homoclinic chaos in a CO2 laser. Phys. Rev. E. 2003;67(1):015205. DOI: 10.1103/PhysRevE.67.015205.
  20. Hirsch JE, Huberman BA, Scalapino DJ. Theory of intermittency. Phys. Rev. A. 1982;25(1):519–532. DOI: 10.1103/PHYSREVA.25.519.
  21. Kye W-H, Kim C-M. Characteristic relations of type-I intermittency in the presence of noise. Phys. Rev. E. 2000;62(5):6304. DOI: 10.1103/PhysRevE.62.6304.
  22. Cho JH, Ko MS, Park YJ, Kim CM. Experimental observation of the characteristic relations of type-I intermittency in the presence of noise. Phys Rev E Stat Nonlin Soft Matter Phys. 2002;65(3):036222. DOI: 10.1103/PhysRevE.65.036222.
  23. Kye WH, Rim S, Kim CM, Lee JH, Ryu JW, Yeom BS, Park YJ. Experimental observation of characteristic relations of type-III intermittency in the presence of noise in a simple electronic circuit. Phys Rev E Stat Nonlin Soft Matter Phys. 2003;68(3):036203. DOI: 10.1103/PhysRevE.68.036203.
  24. Kim C-M, Kwon OJ, Lee Eok-Kyun, Lee Hoyun. New characteristic relations in type-i intermittency. Phys. Rev. Lett. 1994;73(4):525–528. DOI: 10.1103/PhysRevLett.73.525.
  25. Kim C-M, Yim Geo-Su, Ryu Jung-Wan, Park Young-Jai. Characteristic relations of type-iii intermittency in an electronic circuit. Phys. Rev. Lett. 1998;80(24):5317. DOI: 10.1103/PhysRevLett.80.5317.
  26. Hirsch JE, Nauenberg M, Scalapino DJ. Intermittency in the presence of noise: A renormalization group formulation. Phys. Lett. A. 1982;87(8):391–393. DOI: 10.1016/0375-9601(82)90165-7.
  27. Crutchfield JP, Farmer JD, Huberman BA. Fluctuations and simple chaotic dynamics. Physics Reports. 1982;92(2):45–82. DOI: 10.1016/0370-1573(82)90089-8.
  28. Pikovsky AS, Rosenblum MG, Kurths J. Phase synchronisation in regular and chaotic systems. Int. J. Bifurcation and Chaos. 2000;10(10):2291–2305. DOI: 10.1142/S0218127400001481.
  29. 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.
  30. Pikovsky AS, Rosenblum MG, Osipov GV, Kurths J. Phase synchronization of chaotic oscillators by external driving. Physica D. 1997;104(4):219–238. DOI: 10.1016/S0167-2789(96)00301-6.
  31. Rulkov NF, Sushchik MM, Tsimring LS, Abarbanel HDI. Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E. 1995;51(2):980–994. DOI: 10.1103/physreve.51.980.
  32. Pyragas K. Weak and strong synchronization of chaos. Phys. Rev. E. 1996;54(5):R4508-R4511. DOI: 10.1063/1.54216.
  33. Kocarev Lj, Parlitz U. Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Phys. Rev. Lett. 1996;76(11):1816–1819. DOI: 10.1103/PhysRevLett.76.1816.
  34. Abarbanel HDI, Rulkov NF, Sushchik MM. Generalized synchronization of chaos: The auxiliary system approach. Phys. Rev. E. 1996;53(5):4528–4535. DOI: 10.1103/PHYSREVE.53.4528.
  35. Fahy S, Hamann DR. Transition from chaotic to nonchaotic behavior in randomly driven systems. Phys Rev Lett. 1992;69(5):761–764. DOI: 10.1103/PhysRevLett.69.761.
  36. Maritan A, Banavar JR. Chaos, noise, and synchronization. Phys Rev Lett. 1994;72(10):1451–1454. DOI: 10.1103/PhysRevLett.72.1451.
  37. Toral R, Mirasso CR, Hernandez-Garcia E, Piro O. Analytical and numerical studies of noise-induced synchronization of chaotic systems. Chaos. 2001;11(3):665–673. DOI: 10.1063/1.1386397.
  38. Zhou C, Kurths J. Noise-induced phase synchronization and synchronization transitions in chaotic oscillators. Phys Rev Lett. 2002;88(23):230602. DOI: 10.1103/PhysRevLett.88.230602.
  39. Hramov AE, Koronovskii AA, Moskalenko OI. Are generalized synchronization and noise-induced synchronization identical types of synchronous behavior of chaotic oscillators? Phys. Lett. A. 2006;354(5–6):423–427. DOI: 10.1016/j.physleta.2006.01.079.
  40. Pikovsky AS, Rosenblum MG, Kurths J. Synchronization: a universal concept in nonlinear sciences. Cambridge: University Press; 2001. 433 p.
  41. Boccaletti S, Kurths J, Osipov GV, Valladares DL, Zhou CT. The synchronization of chaotic systems. Physics Reports. 2002;366(1-2):1–101. DOI: 10.1016/S0370-1573(02)00137-0.
  42. Hramov AE, Koronovskii AA. Generalized synchronization: a modified system approach. Phys Rev E Stat Nonlin Soft Matter Phys. 2005;71(6):067201. DOI: 10.1103/PhysRevE.71.067201.
  43. Hramov AE, Koronovskii AA. and Moskalenko O.I. Generalized synchronization onset. Europhysics Letters. 2005;72(6):901–907. DOI: 10.1209/epl/i2005-10343-4. DOI: 10.1209/epl/i2005-10343-4.
  44. Hramov AE, Koronovskii AA, Ponomarenko VI, Prokhorov MD. Detecting synchronization of self-sustained oscillators by external driving with varying frequency. Phys Rev E Stat Nonlin Soft Matter Phys. 2006;73(2):026208. DOI: 10.1103/PhysRevE.73.026208.
  45. Hramov AE, Koronovskii AA, Ponomarenko VI, Prokhorov MD. Detection of synchronization from univariate data using wavelet transform. Phys Rev E Stat Nonlin Soft Matter Phys. 2007;75(5):056207. DOI: 10.1103/PhysRevE.75.056207.
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