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Bifurcations of rotating structures in a parabolic functional differential equation

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Nonlinear Oscillations

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.

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Authors and Affiliations

  1. Tavrical National University, Simferopol

    E. P. Belan

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    O. B. Lykova

Authors
  1. E. P. Belan
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  2. O. B. Lykova
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__________

Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 155–169, April–June, 2006.

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Belan, E.P., Lykova, O.B. Bifurcations of rotating structures in a parabolic functional differential equation. Nonlinear Oscill 9, 152–165 (2006). https://doi.org/10.1007/s11072-006-0034-1

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  • DOI: https://doi.org/10.1007/s11072-006-0034-1

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