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Bifurcation of the state of equilibrium of an oscillator with nonlinear restoring force of Third order

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Abstract

Periodic perturbations of the oscillator \(\ddot x\)+ x3 + ax \(\dot x\) = 0, a 2 < 8, are considered. Smallness of perturbations is governed by the smallness of the neighborhood of the state of equilibrium x = 0 and by a small positive parameter. Conditions are given that ensure that an invariant two-dimensional torus branches from the equilibrium when the small parameter passes through the zero value.

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References

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034, Russia

    Yu. N. Bibikov & V. A. Pliss

Authors
  1. Yu. N. Bibikov
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  2. V. A. Pliss
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Correspondence to Yu. N. Bibikov.

Additional information

Original Russian Text © Yu.N. Bibikov, V.A. Pliss, 2015, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2015, No. 2, pp. 171–175.

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Bibikov, Y.N., Pliss, V.A. Bifurcation of the state of equilibrium of an oscillator with nonlinear restoring force of Third order. Vestnik St.Petersb. Univ.Math. 48, 57–60 (2015). https://doi.org/10.3103/S106345411502003X

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  • DOI: https://doi.org/10.3103/S106345411502003X

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