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Van der Pol Oscillator under Random Noise

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Abstract

The first approximations are found to the expectation and the dispersion function of the solution for a mathematical model of an oscillator in the form of a differential equation perturbed by random noise with a small parameter. It is assumed that the perturbations are of random nature without assuming them to be generated by white noise. Resonance conditions for the expectation of the solution are obtained for the harmonic mean value of the perturbing random noise. A new fact is established: the dispersion function increases with increasing time (dispersion resonance) if five algebraic equalities are not satisfied for the moment functions of the random perturbation.

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ACKNOWLEDGMENTS

The author is grateful to Prof. V.G. Zadorozhnii, who predicted the dispersion resonance phenomenon.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620108, Russia

    E. V. Kuptsova

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  1. E. V. Kuptsova
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Correspondence to E. V. Kuptsova.

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Translated by V. Potapchouck

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Kuptsova, E.V. Van der Pol Oscillator under Random Noise. J. Appl. Ind. Math. 16, 449–459 (2022). https://doi.org/10.1134/S1990478922030097

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  • DOI: https://doi.org/10.1134/S1990478922030097

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