Leveraging Real-Time Stochasticity to Detect Transient States in Complex Systems

Detecting transient states and critical transitions in complex systems is essential for predicting abrupt shifts in phenomena such as climate stability, biological health, and financial market trends. However, identifying these transitions in real-time is particularly challenging in noisy, non-stationary data. To address this, we introduce stochasticity, defined as the square of short-term fluctuations within a sliding time window dt [1], as a time-resolved metric for capturing system instability. We demonstrate that stochasticity can serve as a highly sensitive indicator of emerging transient phases, and show that it converges more accurately than traditional drift-based measurements. This approach can identify transitions in diverse domains, including regional temperature anomalies and Parkinson’s disease progression via keystroke dynamics and thus provides a robust tool for monitoring systems where traditional methods struggle to resolve rapid changes.

This project was supported by the Czech Science Foundation, Project No. 25-18105S.

[1] Rahvar, Sepehr, et al. "Characterizing time-resolved stochasticity in non-stationary time series." Chaos, Solitons & Fractals 185 (2024): 115069.