Radiophysics and Quantum Electronics

, Volume 52, Issue 11, pp 832–842 | Cite as

Features of the moment functions of an oscillator with parametric instability due to dichotomous noise with Erlang distribution functions

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We study stability of the periodic solutions of a linear undamped oscillator with frequency modulated by dichotomous noise whose statistic is determined by the Erlang distribution. It is shown that the amplitudes of harmonic oscillations of such an oscillator increase with time at different rates determined by the ratio of the oscillator eigenfrequency to the characteristic frequency of dichotomous noise. To solve the problem, we use a finite system of closed equations with respect to the moment functions, which was obtained without assumption on the quasi-Gaussianity and delta-correlatedness of the studied process.

Keywords

Moment Function State Graph Parametric Instability Golden Ratio Kolmogorov Equation 
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References

  1. 1.
    A. H. Naifeh, Perturbation Methods, Wiley, New York (1973).Google Scholar
  2. 2.
    Ya.G. Panovko, Introduction to the Theory of Mechanical Oscillations [in Russian], Nauka, Moscow (1971).Google Scholar
  3. 3.
    V. V. Bolotin and V. G. Moskvin, Izv. Akad. Nauk SSSR, Mekh. Tver. Tela, No. 4, 88 (1972).Google Scholar
  4. 4.
    J.A.Morrison and J.McKena, J. Math. Phys., 11, 2361 (1970).MATHCrossRefADSGoogle Scholar
  5. 5.
    N. G. van Kampen, Physica, 70, 222 (1973).CrossRefADSGoogle Scholar
  6. 6.
    V. I.Klyatskin, Statistical Description of Dynamical Systems with Fluctuating Parameters [in Russian], Nauka, Moscow (1975).Google Scholar
  7. 7.
    W. Horsthemke and R. Lefever, Noise-Induced Transitions: Theory and Application in Physics, Chemistry, and Biology, Springer-Verlag, Berlin–Heidelberg (1984).Google Scholar
  8. 8.
    N. G. van Campen, Stochastic Processes in Physics and Chemistry, Elsevier, Amsterdam (1981).Google Scholar
  9. 9.
    S.Karlin, A First Course in Stochastic Processes, Academic Press, New York (1968).MATHGoogle Scholar
  10. 10.
    D.König and D. Stoyan, Methoden der Bedienungstheorie, Akademie-Verlag, Berlin (1976).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Research Institute “Tantal”Design Bureau “Progress”SaratovRussia

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