Statistical warning indicators for abrupt transitions in dynamical systems with slow periodic forcing

TL;DR

This paper develops and compares statistical indicators, including phase-based measures, for predicting abrupt transitions in non-autonomous, periodically forced dynamical systems, addressing a gap in existing early warning methods.

Contribution

It introduces phase-based early warning indicators and evaluates their effectiveness in predicting critical transitions in systems with seasonal forcing.

Findings

Phase-based indicators outperform traditional methods in early warning accuracy.

Conventional indicators like variance and autocorrelation are less effective in periodic systems.

The study extends early-warning analysis to non-autonomous dynamical systems with seasonal forcing.

Abstract

There is growing interest in anticipating critical transitions in natural systems, often pursued through statistical detection of early warning signals associated with dynamical bifurcations. In stochastic dynamical systems, such signals commonly rely on manifestations of critical slowing down. However, we still need additional development for the underlying theory for critical transitions in non-autonomous systems. This extension is relevant for natural systems, whose behaviour often emerges from seasonal periodic forcing. In this study, we systematically investigate the feasibility of anticipating the termination of oscillatory behavior in a bistable system with slow periodic forcing. In this setting, existing approaches of estimating linear characteristics of the return map fail in practical scenarios due to the unfavourable time-scale separation. Instead, we propose two statistical indicators for the anticipation of critical transitions in the periodic behaviour: (i) conventional early warning indicators, such as increasing variance and autocorrelation, evaluated across system cycles, and (ii) indicators derived from the phase of the seasonal forcing. By statistically comparing their predictive performance, we find that phase-based indicators provide the strongest early warning capability. Our results offer guidance for the detection of critical transitions in periodically forced systems and, more broadly, systematically extend early-warning signs towards non-autonomous dynamical systems.