Stability of periodic orbits controlled by time-delay feedback
chao-dyn
2009-10-28 v1 Chaotic Dynamics
Abstract
Extended time-delay auto-synchronization (ETDAS) is a promising technique for stabilizing unstable periodic orbits in low-dimensional dynamical systems. The technique involves continuous feedback of signals delayed by multiples of the orbit's period in a manner that is especially well-suited for fast systems and optical implementation. We show how to analyze the stability of a given implementation of ETDAS without explicit integration of time-delay equations. To illustrate the method and point out some nontrivial features of ETDAS, we obtain the domain of control for a period-one orbit of the driven, damped pendulum.
Cite
@article{arxiv.chao-dyn/9510019,
title = {Stability of periodic orbits controlled by time-delay feedback},
author = {Michael E. Bleich and Joshua E. S. Socolar},
journal= {arXiv preprint arXiv:chao-dyn/9510019},
year = {2009}
}
Comments
5 pages REVTeX + 4 PostScript figures, compressed and self-extracting. To appear in Physics Letters A