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arXiv · 1706.06365

Control by time delayed feedback near a Hopf bifurcation point

S. Verduyn Lunel·B. de Wolff
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Abstract

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.

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S. Verduyn Lunel, B. de Wolff. 2017-06-20. Control by time delayed feedback near a Hopf bifurcation point. https://doi.org/10.14232/ejqtde.2017.1.91

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