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.

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

References in corpus (4)

• Dynamics of Limit Cycle Oscillator Subject to General Noise
• Stochastic phase reduction for a general class of noisy limit cycle oscillators
• Phase reduction of stochastic limit cycle oscillators
• Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise

Cited by in corpus (6)

• Interplay of the mechanisms of synchronization by common noise and global coupling for a general class of limit-cycle oscillators
• Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise
• Circular Cumulant Reductions for Macroscopic Dynamics of Kuramoto Ensemble with Multiplicative Intrinsic Noise
• Analytical Phase Reduction for Weakly Nonlinear Oscillators
• Resonances and multistability in a Josephson junction connected to a resonator
• Coherence of Noisy Oscillators with Delayed Feedback Inducing Multistability