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

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.