Anharmonic resonances with recursive delay feedback

Details Anharmonic resonances with recursive delay feedback Anharmonic resonances with recursive delay feedback

2011-05-11

arxiv.org/abs/1105.2226v2

Physics Letters A, Vol. 375, 3410-3414 (2011)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 4 figures, +Maple program and its pdf-print, submitted to Physics Letters A

Scientific paper

10.1016/j.physleta.2011.07.059

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.

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