Dresden 2009 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 26: Poster II
DY 26.12: Poster
Thursday, March 26, 2009, 16:00–18:00, P1A
Control of unstable steady states in neutral time-delayed systems — Yuliya N. Kyrychko1, Konstantin B. Blyuss1, •Philipp Hövel2, and Eckehard Schöll2 — 1Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1TR, UK — 2Institut f. Theo. Physik, Sekr. EW 7-1, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
We present analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. A delay differential equation is called neutral if it contains a time delay in the highest derivative involved. This type of equations arises in numerous physical and engineering application, for example, hybrid testing, chaotic oscillations in transmission lines and torsional waves of a drill string. Due to the original time delay present in the system, its steady states may become unstable through a Hopf bifurcation, and adding a time-delayed feedback control will stabilize the system again
Stability of the controlled system is addressed by studying the eigenvalue spectrum of a corresponding characteristic equation with two time delays. An analytic expression for the stabilizing control strength is derived in terms of original system parameters and the time delay of the control. Theoretical and numerical results show that the interplay between the control strength and two time delays provides a number of regions in the parameter space where the time-delayed feedback control can successfully stabilize an otherwise unstable steady state.