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

For citation:

Semenov V. V., Neiman A. B., Vadivasova T. E., Anishchenko V. S. Noise-induced effects in the double-well oscillator with variable friction. Izvestiya VUZ. Applied Nonlinear Dynamics, 2016, vol. 24, iss. 1, pp. 5-15. DOI: 10.18500/0869-6632-2016-24-1-5-15

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
537.86; 519.21
DOI: 
10.18500/0869-6632-2016-24-1-5-15

Noise-induced effects in the double-well oscillator with variable friction

Autors: 
Semenov V. V., Saratov State University
Neiman Aleksander Borisovich, Ohio University
Vadivasova Tatjana Evgenevna, Saratov State University
Anishchenko Vadim Semenovich, Saratov State University
Abstract: 

A model of bistable stochastic oscillator with dynamical variables depending on dissipation is offered. Considered system demonstrates stochastic P-bifurcations and non-monotonic dependence of the mean oscillation frequency on the noise intensity. An effective noise intensity and an effective potential are introduced for a quantitative description of the observed effects.

Key words: 
bistability
double-well oscillator
noise
stochastic bifurcations
Reference: 
  1. Horsthemke W., Lefever R. Noise-induced Transitions. Berlin: Springer, 1984.
  2. Graham R. Macroscopic potentials, bifurcations and noise in dissipative systems // Noise in Nonlinear Dynamical Systems. Vol.1: Theory of Continuous Fokker-Planck Systems / Ed. by. F. Moss and P.V.E. McClintock. Cambridge: Cambridge University Press, 1989.
  3. Arnold L. Random Dynamical System. Berlin: Springer, 2003.
  4. Sri Namachshivaya N. Stochastic bifurcation// Appl. Math. And Computation. 1990. Vol. 38. P. 101.
  5. Kramers H.A. Brownian motion in a field of force and the diffusion model of chemical reactions // Physica. 1940. Vol. 7. P. 284.
  6. Hanggi P., Talkner P., Borkovec M.  ? Reaction rate theory: Fifty years after Kramers // Rev. Mod. Phys. 1990. Vol. 62. P. 251.
  7. Anishchenko V., Astakhov V., Neiman A., Vadivasova T., Schimansky-Geier L. Nonlinear Dynamics of Chaotic and Stochastic Systems. Second Edition. Berlin: Springer, 2007.
  8. Lindner B., Garcia-Ojalvo J., Neiman A., Schimansky-Geier L. Effects of noise in excitable systems // Physics Reports. 2004. Vol. 392. P. 321.
  9. Gammaitoni L., Marchesoni F., Menichella-Saetta E., Santucci S. Stochastic resonance in bistable systems// Phys. Rev. Lett. 1989. Vol. 62. P. 349.
  10. Anishchenko V.S., Neiman A.B., Moss F., Schimansky-Geier L. Stochastic resonance: Noise-enhanced order// Phys. Usp. 1989. Vol. 42. P. 7.
  11. Pikovsky A., Kurths J. Coherence resonance in a noisy driven excitable system // Phys. Rev. Lett. 1997. Vol. 78. P. 775.
  12. Lindner B., Schimansky-Geier L. Analitical approach to the stochastic FizHugh–Nagumo system and coherence resonance // Phys. Rev. E. 1999. Vol. 60, No 6. P. 7270.
  13. Neiman A.B. Synchronization like phenomena in coupled stochastic bistable systems // Phys. Rev. E. 1994. Vol. 49. P. 3484.
  14. Shulgin B., Neiman A., Anishchenko V. Mean switching frequency locking in stochastic bistable system driven by a periodic force // Phys. Rev. Lett. 1995. Vol. 75, No 23. P. 4157.
  15. 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.
  16. Sanchez E., Mat`ias M.A., Perez-Mu`nuzuri V.  Analysis of synchronization of chaotic systems by noise: An experimental study // Phys. Rev. E. 1997. Vol. 56, No 4. P. 40.
  17. Goldobin D.S., Pikovsky A. Synchronization and desynchronozation of self-sustained oscillators by common noise // Phys. Rev. E. 2005. Vol. 71. P. 045201(4).
  18. Koronovskii A.A., Moskalenko O.I., Trubetskov D.I., Khramov A.E. Generalized synchronization and noise-induced synchronization: the same type of behavior of coupled chaotic systems // Doklady Physics. 2006. Vol. 51. P. 189.
  19. Schimansky-Geier L., Herzel H. Positive Lyapunov exponents in the Kramers oscillator // Journal of Statistical Physiks. 1993. Vol. 70. P. 141.
  20. Arnold L., Imkeller P. Stochastic bifurcation of the noisy Duffing oscillator. Report, Institut fur Dynamische Systeme. Universit at Bremen, 2000.
  21. Freund J.A., Schimansky-Geier L., Hanggi P. Frequency and phase synchronization in stochastic systems // Chaos. 2003. Vol. 13, P. 225.
  22. Rice S.O. Mathematical analysis of random noise // Bell System Tech. J. 1944.  Vol. 23. P. 282. Part 1; 1945. Vol. 24. P. 46. Part 2.
  23. Nikitin N.N., Razevig V.D. Digital simulation of stochastic differential equations and error estimates // USSR Computational Mathematics and Mathematical Physics. 1978. Vol. 18. P. 102.
Received: 
21.12.2015
Accepted: 
23.02.2016
Published: 
28.02.2016
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