Control by time delayed feedback near a Hopf bifurcation point

摘要

In this paper we study the stabilization of rotating waves using time delayedfeedback control. It is our aim to put some recent results in a broader context bydiscussing two different methods to determine the stability of the target periodic orbitin the controlled system: 1) by directly studying the Floquet multipliers and 2) by useof the Hopf bifurcation theorem. We also propose an extension of the Pyragas controlscheme for which the controlled system becomes a functional differential equation ofneutral type. Using the observation that we are able to determine the direction ofbifurcation by a relatively simple calculation of the root tendency, we find stabilityconditions for the periodic orbit as a solution of the neutral type equation.