STOCHASTIC RESONANCE, STOCHASTIC SYNCHRONIZATION AND NOISE-INDUCED CHAOS IN THE DUFFING OSCILLATOR


Cite this article as:

Malyaev V. S., Vadivasova Т. Е., Anishenko V. S. STOCHASTIC RESONANCE, STOCHASTIC SYNCHRONIZATION AND NOISE-INDUCED CHAOS IN THE DUFFING OSCILLATOR. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 5, pp. 74-83. DOI: https://doi.org/10.18500/0869-6632-2007-15-5-74-83


In present paper the following effects in nonlinear oscillator with final dissipation are studied: stochastic resonance, stochastic synchronization and noise-induced chaos. It is shown that stochastic resonance and stochastic synchronization at final dissipation have the same regularities as in the case of overdamped oscillator but are observed at a lower noise level. Equivalent characteristics of potential profile are introduced on the basis of numerically obtained Kramers frequency dependence on noise intensity that allow to apply to considered model the analytical relations, obtained for a overdamped oscillator. It is found that noise-induced transition to chaos in the oscillator with final dissipation can not influence on the stochastic resonance and stochastic synchronization as it is observed in other region of parameter values.

Key words: 
-
DOI: 
10.18500/0869-6632-2007-15-5-74-83
Literature

1. Benzi R., Sutera A., Vulpiani A. The mechanism of stochastic resonance // J. Phys. A: Math. Gen. 1981. Vol. 14. P. L453.

2. Moss F. Stochastic resonance: From the Ice Ages to the Monkey Ear // In: Contemporary Problems in Statistical Physics / ed. by G.H. Weiss. P. 205 (SIAM, Philadelphia, 1994).

3. Gammaitoni L., Marchesoni F., Menichella-Saetta E., Santucci S. Stochastic resonance in bistable systems // Phys. Rev. Lett. 1989. Vol. 62. P. 349.

4. Анищенко В.С., Нейман А.Б., Мосс Ф., Шиманский-Гайер Л. Стохастический резонанс: индуцированный шумом порядок // УФН. 1999. Т. 42, No 1. С. 7.

5. Анищенко В.С., Астахов В.В., Вадивасова Т.Е., Нейман А.Б., Стрелкова Г.И., Шиманский-Гайер Л. Нелинейные эффекты в хаотических и стохастических системах. Москва–Ижевск: Институт компьютерных исследований, 2003.

6. Pikovsky A., Kurths J. Coherence resonance in a noisy driven excitable system// Phys. Rev. Lett. 1997. Vol. 78. P. 775.

7. Neiman A. Saparin P., Stone L. Coherence resonance at noisy precursors of bifurcatuons in nonlinear dynamical systems // Phys. Rev. E. 1997. Vol. 56, No 1. P. 270.

8. Neiman A.B. Synchronizationlike phenomena in coupled stochastic bistable systems // Phys. Rev. E. 1994. Vol. 49. P. 3484.

9. Shulgin B.V., Neiman A.B., Anishchenko V.S. Mean switching frequency locking in stochastic bistable systems driven by periodic force // Phys. Rev. Lett. 1995. Vol. 75. P. 4157.

10. Han S.K., Yim T.G., Postnov D.E., Sosnovtseva O.V. Interacting coherence resonance oscillators // Phys. Rev. Lett. 1999. Vol. 83, No 9. P. 1771.

11. Schimansky-Geier L. and Herzel H. Positive Lyapunov exponents in the Kramers oscillator // Journal of Statistical Physics. 1993. Vol. 70. P. 141.

12. Arnold L., Imkeller P. Stochastic bifurcation of the noisy Duffing oscillator. Report. Institut fur Dynamische Systeme. Universit  ̈ at Bremen, 2000.  ̈

13. Lindner J.F., Meadows B.K., Ditto W.L., Inchiosa M.E., Bulsara A.R. Array enhansed stochastic resonance and spatiotemporal synchronization// Phys. Rev. Lett. 1995. Vol. 75. P. 3.

14. Levin J.E., Miller J.P. Broadband neural encoding in the cricket cercal sensory system enhanced by stochastic resonance // Nature. 1996. Vol. 380. P. 165.

15. Gailey P.C., Neiman A., Collins J.J., Moss F. Stochastic resonance in ensembles of non-dynamical elements. The role of internal noise // Phys. Rev. Lett. 1997. Vol. 79. P. 4701.

16. Zhang Y., Hu G., Gammaitoni L. Signal transmission in one-way coupled bistable systems: Noise effect // Phys. Rev. E. 1998. Vol. 58, No 3. P. 2952.

17. Pei X., Wilkens L., Moss F. Noise-mediated spike timing precision from aperiodic stimuli in an array of Hodgkin–Huxley-type neurons // Phys. Rev. Lett. 1996. Vol. 77, No 2. P. 4679.

18. Neiman A., Pei.X, Russel D.F. et.al Synchronization of the noisy electrosensitive cells in the paddlefish // Phys. Rev. Lett. 1999. Vol. 82, No 3. P. 660.

19. Hu B., Zhou Ch. Phase synchronization in coupled nonidentical excitable systems and array-enhanced coherence resonance // Phys. Rev. E. 2000. Vol. 61, No 2. P. R1001.

20. Климонтович Ю.Л. Что такое стохастическая фильтрация и стохастический резонанс? // УФН. 1999. Т. 169, No 1. С. 39.

21. Kovaleva A. Upper and lower bounds of stochastic resonance and noise-induced synchronization in a bistable oscillator // Phys Rev. E. 2006. Vol. 74. P. 011126(1-5).

22. Hanggi P., Thomas H.  ̈ Stochastic processes: time evolution, symmetries and linear response // Phys. Rep. 1982. Vol. 88. P. 209.

23. Arnold L. Random dynamical systems. Springer-Verlag, Berlin, Heidelberg, New-York, 1998.

Status: 
одобрено к публикации
Short Text (PDF): 
Full Text (PDF): 

BibTeX

@article{Маляев-IzvVUZ_AND-15-5-74,
author = {V. S. Malyaev and Т. Е. Vadivasova and Vadim S. Anishenko},
title = {STOCHASTIC RESONANCE, STOCHASTIC SYNCHRONIZATION AND NOISE-INDUCED CHAOS IN THE DUFFING OSCILLATOR},
year = {2007},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {15},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/stochastic-resonance-stochastic-synchronization-and-noise-induced-chaos-in-the-duffing},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2007-15-5-74-83},pages = {74--83},issn = {0869-6632},
keywords = {-},
abstract = {In present paper the following effects in nonlinear oscillator with final dissipation are studied: stochastic resonance, stochastic synchronization and noise-induced chaos. It is shown that stochastic resonance and stochastic synchronization at final dissipation have the same regularities as in the case of overdamped oscillator but are observed at a lower noise level. Equivalent characteristics of potential profile are introduced on the basis of numerically obtained Kramers frequency dependence on noise intensity that allow to apply to considered model the analytical relations, obtained for a overdamped oscillator. It is found that noise-induced transition to chaos in the oscillator with final dissipation can not influence on the stochastic resonance and stochastic synchronization as it is observed in other region of parameter values. }}