Mode hopping in oscillating systems with stochastic delays

TL;DR

This paper investigates how stochastic delays and phase noise affect a noisy oscillator with pulse delayed feedback, revealing different scaling behaviors and robustness depending on the noise type.

Contribution

It provides a theoretical and experimental analysis of a noisy oscillator with stochastic delays, highlighting the distinct effects of phase noise and delay fluctuations on system stability.

Findings

Robustness to phase noise increases with coupling strength.

Lifetime decreases exponentially with coupling strength under delay fluctuations.

Different noise types lead to distinct scaling properties.

Abstract

We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: i) phase noise acting on the oscillator state variable and ii) stochastic fluctuations of the coupling delay. For both types of stochastic perturbations the system hops between the deterministic regimes, but it shows dramatically different scaling properties for different types of noise. The robustness to conventional phase noise increases with coupling strength. However for stochastic variations in the coupling delay, the lifetimes decrease exponentially with the coupling strength. We provide an analytic explanation for these scaling properties in a linearised model. Our findings thus indicate that the robustness of a system to stochastic perturbations strongly depends on the nature of these perturbations.