Control by time delayed feedback near a hopf bifurcation point

S.M. Verduyn Lunel, B.A.J. de Wolff

Research output: Contribution to JournalArticleAcademicpeer-review


© 2017, University of Szeged. All rights reserved.In this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target periodic orbit in the controlled system: 1) by directly studying the Floquet multipliers and 2) by use of the Hopf bifurcation theorem. We also propose an extension of the Pyragas control scheme for which the controlled system becomes a functional differential equation of neutral type. Using the observation that we are able to determine the direction of bifurcation by a relatively simple calculation of the root tendency, we find stability conditions for the periodic orbit as a solution of the neutral type equation.
Original languageEnglish
Article number91
JournalElectronic Journal of Qualitative Theory of Differential Equations
Publication statusPublished - 1 Jan 2017
Externally publishedYes


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