A dynamic mode decomposition approach to reconstructing networks of coupled oscillators: from periodic to chaotic dynamics
摘要
Network reconstruction of coupled oscillator systems based solely on data poses substantial challenges, especially when the oscillator is chaotic. Conventional approaches relying on similarity measures, causality identification, or parameter inference in dynamic equations encounter limitations in accuracy, computational efficiency, and prior knowledge requirements. To address these limitations, we propose a novel data-driven reconstruction framework that employs dynamic mode decomposition to preprocess the data and focus on a few dominant modes that are correlated with the average frequency of the oscillator. Through a systematic analysis of dynamic mode propagation characteristics-encompassing amplitude attenuation, phase lag, and temporal stability-across oscillator networks, our technique enables the clustering of oscillators with similar dynamic characteristics and infers network topology without requiring many a priori assumptions regarding system dynamics. The proposed framework innovatively constructs a concatenated Hankel matrix from multiple time series, extracts dominant modes via Koopman analysis, and implements a multi-criteria discrimination algorithm for node clustering and edge identification. Comprehensive numerical validation using Kuramoto, FitzHugh–Nagumo, and coupled Lorenz networks demonstrates the framework’s superiority over conventional cross-correlation and coherence techniques, attaining an