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Nonlinear Oscillations

, Volume 9, Issue 2, pp 152–165 | Cite as

Bifurcations of rotating structures in a parabolic functional differential equation

  • E. P. Belan
  • O. B. Lykova
Article

Abstract

We investigate the Andronov-Hopf bifurcation of the birth of a periodic solution from a space-homogeneous stationary solution of the Neumann problem on a disk for a parabolic equation with a transformation of space variables in the case where this transformation is the composition of a rotation by a constant angle and a radial contraction. Under general assumptions, we prove a theorem on the existence of a rotating structure, deduce conditions for its orbital stability, and construct its asymptotic form.

Keywords

Periodic Solution Parabolic Equation Hopf Bifurcation Parabolic Problem Central Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • E. P. Belan
    • 1
  • O. B. Lykova
    • 2
  1. 1.Tavrical National UniversitySimferopol
  2. 2.Institute of MathematicsUkrainian Academy of SciencesKiev

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