Abstract

Critical transitions in many systems cause catastrophic changes. When a control parameter is varied

as a function of time, the rate of change of parameter plays a vital role in the performance of early

warning signals (EWS) for critical transitions. In such cases, memory effects due to continuous

variation of parameter can delay the transition from the bifurcation point. Hence, it is critical to

develop EWS to predict such transitions in practical systems. We study the effect of rate of change

of bifurcation parameter on EWS to predict critical transitions. We find that lag-1 autocorrelation

(AC) and Hurst exponent (H) are better measures compared to other EWS based on critical slowing

down. The warning time estimated using AC and H reduces as we increase the rate of change of

parameter. The warning time follows an inverse power law with the rate of change of parameter.

Consequently, EWS may be too late for very fast rates to perform control action. Furthermore, we

observe a hyperexponential scaling between the variance of fluctuations and AC during this

dynamic bifurcation. We show similar results in a model for noisy Hopf bifurcation wherein the

control parameter is continuously varied at finite rates.