Anharmonic resonances with recursive delay feedback
Abstract
We consider application of the multiple time delayed feedback for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, the multiple one exhibits resonances between feedback and nonlinear harmonics, leading to a resonantly strong or weak oscillation coherence even for a small anharmonicity. Analytical results are confirmed numerically for van der Pol and van der Pol-Duffing oscillators. Highlights: > We construct general theory of noisy limit-cycle oscillators with linear feedback. > We focus on coherence and "reliability" of oscillators. > For recursive delay feedback control the theory shows importance of anharmonicity. > Anharmonic resonances are studied both numerically and analytically.
Cite
@article{arxiv.1105.2226,
title = {Anharmonic resonances with recursive delay feedback},
author = {Denis S. Goldobin},
journal= {arXiv preprint arXiv:1105.2226},
year = {2014}
}
Comments
6 pages, 4 figures, +Maple program and its pdf-print, submitted to Physics Letters A