  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.
