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The capture into parametric autoresonance

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Abstract

In this work, we show that the capture into parametric resonance may be explained as pitchfork bifurcation in the primary parametric resonance equation. We prove that the solution close to the moment of the capture is descibed by the Painlevé-2 equation. We obtain connection formulae for the asymptotic solution of the primary parametric resonance equation before and after the capture using the matching of asymptotic expansions.

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Authors and Affiliations

  1. Institute of Mathematics of USC, Russian Academy of Sciences, Chernyshevsky str. 112, Ufa, 450077, Russia

    O. M. Kiselev

  2. Ufa State Petroleum Technical University, Cosmonavtov str. 1, Ufa, 450062, Russia

    S. G. Glebov

Authors
  1. O. M. Kiselev
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  2. S. G. Glebov
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Correspondence to O. M. Kiselev.

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Kiselev, O.M., Glebov, S.G. The capture into parametric autoresonance. Nonlinear Dyn 48, 217–230 (2007). https://doi.org/10.1007/s11071-006-9084-2

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  • DOI: https://doi.org/10.1007/s11071-006-9084-2

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