Fluctuation-variable correlation as early warning signals of non-equilibrium critical transitions

Complex systems exhibit critical transitions, where the system shifts to a new and radically different state due to external or internal influences. Numerous studies have suggested some indicators to detect the early warning signal of critical transition (tipping point). Nonetheless, these indicators are typically formulated using fixed dynamical models or seldom considered in non-equilibrium natural systems. In this article, we propose a novel indicator, the maximum amplitude Apm, based on the fluctuation-variable correlation. By performing temporal correlation with non-equilibrium dynamic effects and analyzing persistence behavior of dynamics, our findings reveal that Apm increases abruptly and exhibits a peak value that serves as an early warning signal for the impending critical transition. We demonstrate that Apm is a reliable and robust early warning signal by employing three models that presented different types of bifurcations. Additionally, results show that Apm has higher sensitivity and specificity than lag-1 autocorrelation and variance. The indicator also provides early warning signals from the precipitation regime shift event time series of Houston in 2020–2021. Our study contributes to identifying potential critical transitions in natural systems, as well as assisting individuals in better preparing for and avoiding adverse transitions.