Coherence of Noisy Oscillators with Delayed Feedback Inducing Multistability

Anastasiya V Pimenova,Denis S Goldobin

doi:10.1088/1742-6596/681/1/012045

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.

Highlights

Delayed feedback was found to be a highly efficient tool for controlling the coherence of noisy oscillators [1, 2, 3, 4]
In this paper we have developed the theory of the effect of delayed feedback on coherence of noisy phase oscillators in the presence of frequency multistability induced by this time delay
The process of alternation between two states has been demonstrated to be well representable as an asymmetric Markovian ‘telegraph’ process

Summary

Introduction

Delayed feedback was found to be a highly efficient tool for controlling the coherence of noisy oscillators [1, 2, 3, 4]. Dynamics of the system subject to weak noise Let us rewrite equation (1) in the form ω(t) ≡ φ = Ω0 − a sin β(t) + εξ(t) , β(t) = ω(t) − ω(t − τ ) , where β ≡ φ(t) − φ(t − τ ) is the phase growth per delay time. This integral form of our dynamic system suggests that β(t) can be a suitable ‘natural’ variable to trace the switchings between two states.

Phase diffusion on the edges of the multistability domains

Behaviour of phase diffusion near the centres of the multistability domains

Conclusion