An odd-number limitation of extended time-delayed feedback control in autonomous systems
Chaotic Dynamics
2015-06-16 v1
Abstract
We propose a necessary condition for the successful stabilisation of a periodic orbit using the extended version of time-delayed feedback control. This condition depends on the number of real Floquet multipliers larger than unity and is therefore related to the well-known odd-number limitation in non-autonomous systems. We show that the period of the orbit which is induced by mismatching the delay-time of the control scheme and the period of the uncontrolled orbit plays an important role in the formulation of the odd-number limitation in the autonomous case.
Keywords
Cite
@article{arxiv.1307.8316,
title = {An odd-number limitation of extended time-delayed feedback control in autonomous systems},
author = {Andreas Amann and Edward W. Hooton},
journal= {arXiv preprint arXiv:1307.8316},
year = {2015}
}