Control by time delayed feedback near a Hopf bifurcation point
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.
Cite
@article{arxiv.1706.06365,
title = {Control by time delayed feedback near a Hopf bifurcation point},
author = {S. Verduyn Lunel and B. de Wolff},
journal= {arXiv preprint arXiv:1706.06365},
year = {2018}
}
Comments
20 pages