2025/05/07 by Yiting Duan, Duan, Yiting, Yi Guo +5
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.2505.04815
openalex publication_date 2025/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper systematically discusses how the inherent properties of chaotic attractors influence the results of discovering causality from time series using convergent cross mapping, particularly how convergent cross mapping misleads bidirectional causality as unidirectional when the chaotic attractor exhibits symmetry. We propose a novel method based on the k-means clustering method to address the challenges when the chaotic attractor exhibits two-fold rotation symmetry. This method is demonstrated to recover the symmetry of the latent chaotic attractor and discover the correct causality between time series without introducing information from other variables. We validate the accuracy of this method using time series derived from low-dimension and high-dimensional chaotic symmetric attractors for which convergent cross mapping may conclude erroneous results.