Coherence versus reliability of stochastic oscillators with delayed feedback

Abstract

For noisy self-sustained oscillators, both reliability, stability of a response to a noisy driving, and coherence understood in the sense of constancy of oscillation frequency belong to the main characteristics. Though the both characteristics and techniques for controlling them received great attention of researchers, owing to their importance for neurons, lasers, clocks, electric generators, etc., these characteristics were previously considered separately. In this paper, strong quantitative relation between coherence and reliability is revealed for a limit cycle oscillator subject to a weak noisy driving and a linear delayed feedback, a convectional control tool. Analytical findings are verified and enriched with a numerical simulation for the Van der Pol-Duffing oscillator.

4 pages, 5 figures

References in corpus (5)

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Cited by in corpus (8)

• Dynamics of Limit Cycle Oscillator Subject to General Noise
• Stochastic phase reduction for a general class of noisy limit cycle oscillators
• Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise
• Anharmonic resonances with recursive delay feedback
• Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise
• Anomalous Consistency in Mild Cognitive Impairment: a complex networks approach
• Two scenarios of advective washing-out of localized convective patterns under frozen parametric disorder
• Noise Can Reduce Disorder in Chaotic Dynamics