2021/09/15 by Suddhasattwa Das, Das, Suddhasattwa, Shakib Mustavee +3
Computer Science · Physics and Astronomy · #37M10 #37M25 #47A35 #Chaotic Dynamics (nlin.CD) #Computational Physics and Python Applications #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Model Reduction and Neural Networks #Scientific Research and Discoveries
paper · pdf · doi:10.48550/arxiv.2109.08623
openalex publication_date 2021/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a novel approach to analyze quasiperiodically driven dynamical systems. It aims to develop a complete data-driven framework for modeling such unknown dynamics. To achieve this, we characterize Koopman eigenfrequencies as generating frequencies of the quasiperiodic driver of the system. We compute true eigenfrequencies of Koopman operators by applying the theory of Reproducing Kernel Hibert Space (RKHS) and results from ergodic theory. We also demonstrate the decomposition of quasiperiodically driven dynamics into two components, i) the quasiperiodic driving source with generating frequencies and ii) the driven nonlinear dynamics. A unique aspect of the proposed framework is that it applies to the analysis of systems where the periodic component is either non-dominant or even absent. As a case study, we analyze a system of nine traffic signalized intersections. The proposed framework accurately reconstructs the measured queue lengths of the signalized intersections and makes stable long-term predictions.