Modulating coherence resonance in non-excitable systems by time-delayed feedback

TL;DR

This paper investigates how time-delayed feedback influences coherence resonance in non-excitable systems using a subcritical Hopf model with noise, developing analytical tools to quantify the phenomenon.

Contribution

It introduces a new analytical approach to estimate stationary distributions and correlations in stochastic delay differential equations, and proposes a novel measure for coherence resonance.

Findings

Time delay significantly modulates coherence resonance effects.

Analytical tools effectively predict system behavior under noise and delay.

A new measure accurately captures coherence resonance induced by bifurcations.

Abstract

We propose a paradigmatic model system, a subcritical Hopf normal form subjected to noise and time-delayed feedback, to investigate the impact of time delay on coherence resonance in non-excitable systems. We develop analytical tools to estimate the stationary distribution and the time correlations in nonlinear stochastic delay differential equations. These tools are applied to our model to propose a novel quantity to measure coherence resonance induced by a saddle-node bifurcation of periodic orbits.