Critical speeding up as an early warning signal of regime switching (1901.08084v1)

Abstract: The use of critical slowing down as an early warning indicator for regime switching in observations from stochastic environments and noisy dynamical models has been widely studied and implemented in recent years. Some systems, however, have been shown to avoid critical slowing down prior to a transition between equilibria, e.g. (Ditlevsen and Johnsen, 2010). Possible explanations include non-smooth potential driving the dynamic (Hastings and Wysham, 2010) or large perturbations driving the system out of the initial basin of attraction. In this paper we discuss a phenomenon analogous to critical slowing down, where a slow parameter change leads to a high likelihood of a regime shift and creates signature warning signs in the statistics of the process's sample paths. In short, if a basin of attraction is compressed under a parameter change then the potential well steepens, leading to a drop in the time series' variance and autocorrelation; precisely the opposite warning signs exhibited by critical slowing down. This effect, which we call `critical speeding up,' is demonstrated using a simple ecological model exhibiting an Allee effect. The fact that both dropping and rising variance / autocorrelation can indicate imminent state change should underline the need for reliable modeling of any empirical system where one desires to forecast regime change.