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Random oscillations in the Van der Pol system under the action of a broadband random process

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Abstract

We construct the second approximation for random oscillations described by the Van der Pol equation which are under the action of a broadband random process.

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References

  1. N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in Nonlinear Mechanics [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  2. Yu. A. Mitropol’skii, Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka (1971).

  3. Yu. A. Mitropol’skii, Nguyen Van Dao, and Nguyen Dong Anh, Nonlinear Oscillations in Systems of Arbitrary Order [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

  4. R. V. Roy and R. D. Spanos, “Pade-type approach to non-linear random vibration analysis,” Prob. Eng. Mech., 6, No. 3, 4, 119–128 (1991).

    Article  Google Scholar 

  5. Yu. A. Mitropol’skii, Nonlinear Mechanics. Asymptotic Methods [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1995).

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  6. Nguyen Dong Anh, “Higher approximate solutions in stochastic averaging method,” Proc NCSR NV, 5, No 1, 19–26 (1993).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1517–1521, November, 1998.

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Mitropol’skii, Y.A., Anh, N.D. & Tynh, N.D. Random oscillations in the Van der Pol system under the action of a broadband random process. Ukr Math J 50, 1731–1737 (1998). https://doi.org/10.1007/BF02524479

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  • DOI: https://doi.org/10.1007/BF02524479

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