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

For citation:

Semenov V. V. Experimental research of self-oscillation destruction under additive noise action. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 3, pp. 43-51. DOI: 10.18500/0869-6632-2013-21-3-43-51

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 151)
Article type: 

Experimental research of self-oscillation destruction under additive noise action

Semenov V. V., Saratov State University

Evolution of probabilistic distribution in self-sustained oscillators with increase of noise intensity is studied by means of numerical simulation and natural experiments. Two different systems are considered: van der Pol and Anishchenko–Astakhov self-sustained oscillators. Destruction of probabilistic distribution form, which is typical for noisy selfoscillation, by additive noise is showed.

  1. Benzi R, Sutera A, Vulpiani A. The mechanism of stochastic resonance. J. Phys. A: Math. Gen. 1981;14(11):L453. DOI:10.1088/0305-4470/14/11/006.
  2. Gammaitoni L, Marchesoni F, Menichella-Saetta E, Santucci S. Stochastic resonance in bistable systems. Phys. Rev. Lett. 1989;62(4):349–352. DOI: 10.1103/PhysRevLett.62.349.
  3. Anishchenko VS, Neiman AB, Moss F, Shimansky-Geier L. Stochastic resonance: noise-enhanced order. Phys. Usp. 1999;42(1):7–36.
  4. Pikovsky A, Kurths J. Coherence resonance in a noisy driven excitable system. Phys. Rev. Lett. 1997;78(5):775–778. DOI:10.1103/PHYSREVLETT.78.775.
  5. Lindner B, Schimansky-Geier L. Analytical approach to thе stochastic FizHugh–Nagomo system and coherence resonance. Phys. Rev. E. 1999;60(6):7270–7276. DOI: 10.1103/physreve.60.7270.
  6. Neiman AB. Synchronizationlike phenomena in coupled stochastic bistable systems. Phys. Rev. E. 1994;49(4):3484–3487. DOI: 10.1103/physreve.49.3484.
  7. Shulgin B, Neiman A, Anishchenko V. Mean switching frequency locking in stochastic bistable system driven by a periodic force. Phys. Rev. Lett. 1995;75(23):4157–4160. DOI: 10.1103/PhysRevLett.75.4157.
  8. Han SK, Yim TG, Postnov DE, Sosnovtseva OV. Interacting coherence resonance oscillators. Phys. Rev. Lett. 1999;83(9):1771–1774. DOI:10.1103/PhysRevLett.83.1771.
  9. Dmitriev BS, Zharkov JD, Sadovnikov SA, Skorohodov VN. Synchronization of klystron oscillator with delayed feedback in the presence of noise. Izvestiya VUZ. Applied Nonlinear Dynamics. 2011;19(5):17-26. DOI: 10.18500/0869-6632-2011-19-5-17-26.
  10. Anishchenko VS, Safonova MA. Noise-induced exponential dispersion of phase trajectories near regular attractors. Pisma v Zhurnal Tekhnicheskoi Fiziki. 1986;12(12):740–744.
  11. Ebeling W, Herzel H, Richert W, Schimansky-Geier L. Influence of noise on Duffing – van der Pol oscillators. Zeischrift fur angewandte Мathematik und Mechanik. 1986;66(3):141–146. DOI:10.1002/zamm.19860660303.
  12. Schimansky-Geier L, Herzel H. Positive Lyapunov exponents in the Kramers oscillator. J. Stat. Phys. 1993;70:141–147. DOI:10.1007/BF01053959.
  13. Koronovskii AA. et al. Generalized synchronization and noise-induced synchronization: The same type of behavior of coupled chaotic systems. Doklady Physics. 2006;51(4):189–192. DOI: 10.1134/S1028335806040070.
  14. Dmitriev BS, Zharkov YD, Koronovsky AA, Hramov AE, Skorokhodov VN. Experimental and theoretical investigations of the influence of the external noise on dynamics of a klystron oscillator. Journal of Communications Technology and Electronics. 2012;57(1):45–53. DOI: 10.1134/S1064226912010056.
  15. Goldobin DS, Pikovsky A. Synchronization and desynchronization of self-sustained oscillators by common noise. Phys. Rev. E. 2005;71(4):045201. DOI: 10.1103/PhysRevE.71.045201.
  16. Horsthemke B, Lefebvre R. Noise-induced transitions. Moscow: Mir; 1987. 400 p. (In Russian).
  17. Arnold L. Random Dynamical System. Berlin: Springer; 2003. 591 p.
  18. Lefever R, Turner J. Sensitivity of a Hopf bifurcation to multiplicative colored noise. Phys. Rev. Lett. 1986;56(16):1631–1634. DOI: 10.1103/PhysRevLett.56.1631.
  19. Olarrea J, de la Rubia FJ. Stochastic Hopf bifurcation: The effect of colored noise on the bifurcational interval. Phys. Rev. E. 1996;53(1):268–271. DOI: 10.1103/physreve.53.268.
  20. Arnold L, Sri Namachshivaya N, Schenk-Yoppe KR. Toward an understanding of stochastic Hopf bifurcation: А base study. Int. J. Bifurcation and Chaos. 1996;6(11):1947–1975.
  21. Bashkirtseva I, Ryashko L, Schurz H. Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances. Chaos, Solitons, and Fractals. 2009;39(1):72–82. DOI:10.1016/j.chaos.2007.01.128.
  22. Zakharova A, Vadivasova T, Anishchenko V, Koseska A, Kurths J. Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator. Phys. Rev. E. 2010;81(1):011106. DOI:10.1103/PhysRevE.81.011106.
  23. Franzoni L, Mannella R, McClintock P, Moss F. Postponement of Hopf bifurcations by multiplicative colored noise. Phys. Rev. F. 1987;36(2):834–841. DOI:10.1103/PhysRevA.36.834.
  24. Anishchenko VS. Complex fluctuations in simple systems. Moscow: URSS; 2009. 314 p. (In Russian).
Short text (in English):
(downloads: 58)