  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.
