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


For citation:

Zhuravlev M. O., Koronovskii A. A., Moskalenko O. I., Hramov A. E. STATISTICAL CHARACTERISTICS OF NOISE-INDUCED INTERMITTENCY IN MULTISTABLE SYSTEMS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2018, vol. 26, iss. 1, pp. 80-89. DOI: 10.18500/0869-6632-2018-26-1-80-89

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: 93)
Полный текст в формате PDF(En):
(downloads: 50)
Language: 
Russian
Heading: 
Article type: 
Article
UDC: 
530.182

STATISTICAL CHARACTERISTICS OF NOISE-INDUCED INTERMITTENCY IN MULTISTABLE SYSTEMS

Autors: 
Zhuravlev Maksim Olegovich, Saratov State University
Koronovskii Aleksei Aleksandrovich, Saratov State University
Moskalenko Olga Igorevna, Saratov State University
Hramov Aleksandr Evgenevich, Innopolis University
Abstract: 

The paper is devoted to the study of noise-induced intermittent behavior in multistable systems. Such task is an important enough because despite of a great interest of investigators to the study of multistability and intermittency, the problem connected with the detailed understanding of the processes taking place in the multistable dynamical systems in the presence of noise and theoretical description of arising at that intermittent behavior is still remain unsolved. In present paper we analyze the noise-induced intermittency in multistable systems using the examples of model bistable system being under influence of external noise and two dissipatively coupled logistic maps subjected to additional noise. We have shown that the influence of noise on multistable system for certain values of the control parameters results in the appearance of noise-induced intermittent behavior. At that, for the found type of intermittent behavior the analytical relations for residence time distributions and dependence of the mean length of the residence times on the criticality parameter have been obtained. During the numerical simulations carried out we have found statistical characteristics for such type of intermittency for both systems, i.e. the distributions of the residence times for both coexisting stable states as well as the dependence of the mean length of the residence times for both regimes on the criticality parameter. The results of numerical simulation of intermittent behavior for systems under study have been compared with the obtained analytical regularities for noise-induced intermittency in multistable systems. At that, we have shown that numerical results and theoretical regularities are in a good agreement with each other.

Reference: 
  1. Berge P., Pomeau Y., Vidal C. Order within Chaos. New York: John Wiley and Sons, 1984.
  2. Dremin I.M. Intermittence and fractal dimensionality in multiple particle creation processes. Physics–Uspekhi, 1987. vol. 30, pp. 649–653.
  3. Shandarin S.F., Doroshkevich A.G., Zel’dovich Ya.B. The large-scale structure of the universe. Physics–Uspekhi, 1983, vol. 26, pp. 46–76.
  4. Hammer P.W., Platt N., Hammel S.M., Heagy J.F., Lee B.D. Experimental observation of on–off intermittency. Phys. Rev. Lett., 1994, vol. 73, p. 1095.
  5. Heagy J.F., Platt N., Hammel S.M. Characterization of on–off intermittency. Phys. Rev. E, 1994, vol. 49, p. 1140.
  6. Pikovsky A.S., Osipov G.V., Rosenblum M.G., Zaks M., Kurths J. Attractor–repeller collision and eyelet intermittency at the transition to phase synchronization. Phys. Rev. Lett., 1997, vol. 79, p. 47.
  7. Hramov A.E., Koronovskii A.A., Kurovskaya M.K., Boccaletti S. Ring intermittency in coupled chaotic oscillators at the boundary of phase synchronization. Phys. Rev. Lett., 2006, vol. 97, p. 114101.
  8. Kye W.-H., Kim C.-M. Characteristic relations of type-I intermittency in the presence of noise. Phys. Rev. E, 2000, vol. 62, p. 6304.
  9. Huerta-Cuellar G., Pisarchik A.N., Barmenkov Y.O. Experimental characterization of hopping dynamics in a multistable fiber laser. Phys. Rev. E, 2008, vol. 78, p. 35202.
  10. Kraut S., Feudel U. Multistability, noise, and attractor hopping: The crucial role of chaotic saddles. Phys. Rev. E, 2002, vol. 66, p. 15207.
  11. Arecchi F.T., Badii R., Politi A. Generalized multistability and noise-induced jumps in a nonlinear dynamical system. Phys. Rev. A, 1985, vol. 32, p. 402.
  12. Wiesenfeld K., Hadley P. Attractor crowding in oscillator arrays. Phys. Rev. Lett., 1989, vol. 62, p. 1335.
  13. Pisarchik A.N., Jaimes-Reategui R., Sevilla-Escoboza R., Huerta-Cuellar G., Taki M. Rogue waves in a multistable system. Phys. Rev. Lett., 2011, vol. 107, p. 274101.
  14. Pikovsky A.S., Zaks M., Rosenblum M.G., Osipov G.V., Kurths J. Phase synchronization of chaotic oscillators in terms of periodic orbits. Chaos, 1997, vol. 7, p. 680.
  15. Astakhov V.V., Bezruchko B.P., Gulyaev Yu.V., Seleznev E.P. Technical Physics Letters, 1989, vol. 15, p. 60.
  16. Poston T., Stewart I. Catastrophe Theory and its Applications. Pitman, 1978.
  17. Kuznetsov S.P. Dynamical Chaos. Moscow: Fizmatlit, 2001 (in Russian).
  18. Koronovskii A.A., Hramov A.E. Type-II intermittency characteristics in the presence of noise. Eur. Phys. J. B., 2008, vol. 62, p. 447.
  19. Runnova A.E., Hramov A.E., Grubov V.V., Koronovsky A.A., Kurovskaya M.K., Pisarchik A.N. Theoretical background and experimental measurements of human brain noise intensity in perception of ambiguous images. Chaos, Solitons & Fractals, 2016, vol. 93, p. 201.
  20. Kramers H.A. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica, 1940, vol. 7, p. 284.
Received: 
25.10.2017
Accepted: 
28.12.2017
Published: 
28.02.2018
Short text (in English):
(downloads: 0)