Anharmonic resonances with recursive delay feedback

We consider application of time-delayed feedback with infinite recursion for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, recursive delay feedback exhibits resonances between feedback and nonlinear harmonics, leading to a resonan...

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Bibliographic Details
Published in:Physics letters. A 2011-09, Vol.375 (39), p.3410-3414
Main Author: Goldobin, Denis S.
Format: Article
Language:English
Subjects:
Anharmonicity
Control
Control systems
Control theory
Delay
Feedback
Noisy oscillators
Nonlinearity
Oscillators
Recursive
Recursive delay feedback
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Summary:We consider application of time-delayed feedback with infinite recursion for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, recursive delay feedback exhibits resonances between feedback and nonlinear harmonics, leading to a resonantly strong or weak oscillation coherence even for a small anharmonicity. Remarkably, these small-anharmonicity induced resonances can be stronger than the harmonic ones. Analytical results are confirmed numerically for van der Pol and van der Pol–Duffing oscillators. ► 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.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2011.07.059