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


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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

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Russian
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Article
UDC: 
537.86/.87:530.182

Experimental research of self-oscillation destruction under additive noise action

Autors: 
Semenov V. V., Saratov State University
Abstract: 

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.

Reference: 
  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).
Received: 
13.03.2013
Accepted: 
18.04.2013
Published: 
31.10.2013
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