Ukrainian Mathematical Journal

, Volume 67, Issue 7, pp 1008–1037 | Cite as

Dynamical Bifurcation of Multifrequency Oscillations in a Fast-Slow System

  • A. M. Samoilenko
  • I. O. Parasyuk
  • B. V. Repeta

We study a dynamical analog of bifurcations of invariant tori for a system of interconnected fast phase variables and slowly varying parameters. It is shown that, in this system, due to the slow evolution of the parameters, we observe the appearance of transient processes (from the damping process to multifrequency oscillations) asymptotically close to motions on the invariant torus.


Invariant Manifold Invariant Torus Local Attractor Dynamical Analog Dynamical Bifurcation 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • A. M. Samoilenko
    • 1
  • I. O. Parasyuk
    • 2
  • B. V. Repeta
    • 2
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine
  2. 2.Shevchenko Kyiv National UniversityKyivUkraine

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