Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

TL;DR

This study investigates how the rate of parameter change affects the delay in critical transitions in stochastic systems, demonstrating experimentally and through modeling that faster changes lead to larger delays and hysteresis effects.

Contribution

It provides the first experimental evidence and modeling of rate-dependent bifurcation delay in stochastic systems, emphasizing its importance in predicting critical transitions.

Findings

Rate-dependent bifurcation delay increases with the rate of parameter change.

Faster parameter ramps cause larger amplitude state transitions.

Experimental evidence of dynamic hysteresis due to bifurcation delay.

Abstract

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared to the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinise the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points and it pinpoints the crucial need of considering this effect when investigating critical transitions.