Coherence of Noisy Oscillators with Delayed Feedback Inducing Multistability

TL;DR

This paper investigates how delayed feedback-induced multistability affects the coherence of noisy self-sustained oscillators, combining numerical and analytical methods to understand the interplay between delay, multistability, and coherence.

Contribution

It provides a novel analysis of the influence of delay-induced multistability on oscillator coherence, extending understanding of feedback control in noisy systems.

Findings

Delayed feedback enhances coherence for longer delays.

Multistability arises in noise-free oscillators with long delays.

Multistability impacts phase diffusion and coherence in noisy oscillators.

Abstract

For self-sustained oscillators subject to noise the coherence, understood as a constancy of the instantaneous oscillation frequency, is one of the primary characteristics. The delayed feedback has been previously revealed to be an efficient tool for controlling coherence of noise-driven self-sustained oscillator. The effect of the delayed feedback control on coherence is stronger for a longer delay time. Meanwhile, the instantaneous frequency of a noise-free oscillator can exhibit multistability for long delay time. The impact of the delay-feedback--induced multistability on the oscillation coherence, measured by the phase diffusion constant, of a noisy oscillator is studied in this work both numerically and analytically.