动态系统中慢周期驱动下突变转变的统计预警指标
Statistical warning indicators for abrupt transitions in dynamical systems with slow periodic forcing
AI总结：
研究探讨了在慢周期驱动的双稳系统中，通过统计指标预测振荡行为终止的可行性，提出基于季节性驱动相位的预警指标，发现其具有最强的预警能力。
摘要：
近年来，人们对预测自然系统中临界转变的兴趣日益增长，通常通过统计检测与动态分岔相关的早期预警信号来实现。在随机动态系统中，此类信号通常依赖于临界减慢的表现。然而，对于非自治系统中临界转变的底层理论仍需进一步发展。这种扩展对于自然系统尤为重要，因为其行为往往源于季节性周期驱动。在本研究中，我们系统地探讨了在慢周期驱动的双稳系统中预测振荡行为终止的可行性。在该设定中，现有方法在实际场景中因时间尺度分离不利而失效。相反，我们提出了两种统计指标用于预测周期行为中的临界转变：(i) 传统的早期预警指标，如方差和自相关性的增加，跨系统周期评估；(ii) 从季节性驱动相位导出的指标。通过统计比较其预测性能，我们发现基于相位的指标具有最强的预警能力。我们的结果为周期驱动系统的临界转变检测提供了指导，并更广泛地将早期预警信号扩展到非自治动态系统。
英文摘要：
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.
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