Early-warning signals of critical transition: Effect of extrinsic noise

Abstract

Complex dynamical systems often have tipping points and exhibit catastrophic regime shift. Despite the notorious difficulty of predicting such transitions, accumulating studies have suggested the existence of generic early-warning signals (EWSs) preceding upcoming transitions. However, previous theories and models were based on the effect of the intrinsic noise (IN) when a system is approaching a critical point, and did not consider the pervasive environmental fluctuations or the extrinsic noise (EN). Here, we extend previous theory to investigate how the interplay of EN and IN affects EWSs. Stochastic simulations of model systems subject to both IN and EN have verified our theory and demonstrated that EN can dramatically alter and diminish the EWS. This effect is stronger with increasing amplitude and correlation time scale of the EN. In the presence of EN, the EWS can fail to predict or even give a false alarm of critical transitions.

Detecting and distinguishing tipping points using spectral early warning signals

“…As such, EWS that are specific to each type of bifurcation are required to predict ensuing dynamics. Moreover, external noise that is correlated or density dependent can distort EWS [19,20], so there is a need to develop metrics that are more robust to these forms of noise.…”

“…This way, one can move beyond generic indicators of an upcoming transition (which do not always behave as expected), towards more reliable indicators that are specific to the system being modelled. This analytical approach was recently adopted in previous studies to investigate the behaviour of EWS specific to particular models [31,32], and different regimes of noise [20,28]. It has also been used to derive EWS approximations for a subset of local bifurcations in continuous-time [28] and analytical approximations of the power spectrum prior to continuous-time bifurcations of period orbits [21].…”

A systematic study of the determinants of protein abundance memory in cell lineage

“…Because intrinsic noise and extrinsic noise may have different effects on protein memory in the cell lineage [5], we first investigated a system with intrinsic noise only. The dynamics of protein concentration follows the stochastic differential equation (SDE) [23,24] dXðtÞ dt…”

“…We first incorporated extrinsic noise into the production rate [27]. We assumed that the fluctuation of the production rate k p was described by the following equation [15,24,28,29…”

“…In this case, we had D ¼ 2k p , where parameter k p is the production rate, and r 2 ex ¼ k pp s, where k pp and 1=s is the birth and death terms of production rate (Eq. (3)) [24,33] (see Supplementary Materials for details).…”