Cybernetics and Systems Analysis

, Volume 51, Issue 3, pp 400–409 | Cite as

Analysis of Fluctuations of a Parametric Vacuum Tube Oscillator with Delayed Feedback

  • V. K. Yasynskyy
  • I. V. Malyk


The generating equation and equations for amplitude and phase fluctuations of the parametric tube oscillator with delayed feedback are analyzed in the paper. The steady-state oscillation modes and the influence of fluctuations in the natural frequency of the oscillator on the operation of the self-oscillator and parametric “pumping” in the presence of interference are investigated. The domains for the parameters of the original equation corresponding to unstable nodes, stable nodes, and focal points are identified.


vacuum tube oscillator parametric “pump,” steady state mode 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. I. Bukatar’ and E. F. Tsar’kov, “Self-oscillations in a vacuum tube oscillator with delayed feedback,” Izvestiya Vuzov, No. 8, 1117–1125 (1970).Google Scholar
  2. 2.
    I. S. Gonorovskii, “To the theory of high-frequency oscillators with delayed feedback,” Radiotekhnika, 13, No. 5, 19–30 (1958).Google Scholar
  3. 3.
    R. A. Stratonovich, Selected Issues from the Theory of Fluctuations in Radio Engineering [in Russian], Sov. Radio, Moscow (1961).Google Scholar
  4. 4.
    E. F. Tsar’kov, Random Perturbations of Functional Differential Equations [in Russian], Zinatne, Riga (1989).Google Scholar
  5. 5.
    V. P. Rubanik, Oscillations of Quasilinear Systems with Delay [in Russian], Nauka, Moscow (1969).Google Scholar
  6. 6.
    V. K. Yasinsky and I. V. Malyk, “Parametric continuity of solutions to stochastic functional differential equations with Poisson perturbations,” Cybern. Syst. Analysis, 48, No. 6, 846–860 (2012).MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    V. K. Yasinsky and I. V. Malyk, “Analysis of oscillations in quasilinear stochastic dynamic hereditary systems,” Cybern. Syst. Analysis, 49, No. 3, 397–408 (2013).MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, Springer, Berlin (1987).MATHCrossRefGoogle Scholar
  9. 9.
    P. Billingsley, Convergence of Probability Measures, Wiley-Interscience (1999).Google Scholar
  10. 10.
    A. A Jakubovski, “Non-Skorohod topology on the Skorohod space,” Electronic J. of Probability, 42, No. 18, 1–21 (1997).Google Scholar
  11. 11.
    I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and their Applications [in Russian], Naukova Dumka, Kyiv (1982).Google Scholar
  12. 12.
    R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York (1963).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Yuriy Fedkovych Chernivtsi National UniversityChernivtsiUkraine

Personalised recommendations