Coherence versus reliability of stochastic oscillators with delayed feedback

TL;DR

This paper explores the quantitative relationship between coherence and reliability in noisy oscillators with delayed feedback, providing analytical and numerical insights relevant to various physical and biological systems.

Contribution

It reveals a strong quantitative relation between coherence and reliability in oscillators with delayed feedback, combining analytical and numerical methods.

Findings

Analytical expressions linking coherence and reliability.

Numerical verification using Van der Pol-Duffing oscillator.

Delayed feedback influences both coherence and reliability.

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.