2024/07/18 by Bulcsú Sándor, Sándor, Bulcsú, A. Rusu +7
Computer Science · Economics, Econometrics and Finance · #37N99 #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #Data Analysis #FOS: Physical sciences #Statistics and Probability (physics.data-an) #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.2407.13452
openalex publication_date 2024/07/18 · openalex created_date 2025/01/04 · openalex updated_date 2026/07/28
There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the underlying chaotic systems is a notoriously difficult task. Building on prior theoretical studies that focus on the discontinuities at q=1 in the order-q Rényi-entropy of the trajectory space, we measure the derivative of the spectrum. We derive within the general context of Markov processes a computationally efficient closed-form expression for this measure. We investigate its properties through well-known dynamical systems exploring its scope and limitations. The proposed mathematical instrument can serve as a predictor of dynamical phase transitions in time series.