Changes in the timescales at which complex systems evolve are essential to predicting critical transitions and catastrophic failures. Disentangling the timescales of the dynamics governing complex systems remains a key challenge. With this study, we introduce an integrated Bayesian framework based on temporal network models to address this challenge. We focus on two methodologies: change point detection for identifying shifts in system dynamics, and a spectrum analysis for inferring the distribution of timescales. Applied to synthetic and empirical datasets, these methologies robustly identify critical transitions and comprehensively map the dominant and subsidiaries timescales in complex systems. This dual approach offers a powerful tool for analyzing temporal networks, significantly enhancing our understanding of dynamic behaviors in complex systems.

翻译：复杂系统演化时间尺度的变化对于预测临界转变和灾难性失效至关重要。解缠控制复杂系统动力学的多时间尺度仍是一项关键挑战。本研究提出一种基于时间网络模型的集成贝叶斯框架来应对这一挑战。我们聚焦于两种方法论：用于识别系统动力学转变的变点检测，以及用于推断时间尺度分布的频谱分析。将这两种方法应用于合成数据集与经验数据集，能够稳健地识别临界转变，并全面映射复杂系统中的主要时间尺度与次要时间尺度。这种双重视角方法为分析时间网络提供了强大工具，显著增强了对复杂系统动态行为的理解。