2023/08/12 by Natsuki Tsutsumi, Tsutsumi, Natsuki, Kengo Nakai +3
Computer Science · Physics and Astronomy · #37Mxx #37Nxx #65Txx #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #Data Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Neural Networks and Applications #Statistics and Probability (physics.data-an) #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.2308.12382
openalex publication_date 2023/08/12 · openalex created_date 2023/08/26 · openalex updated_date 2026/07/28
In our previous study (N. Tsutsumi, K. Nakai and Y. Saiki (2022)) we proposed a method of constructing a system of differential equations of chaotic behavior only from observable deterministic time series, which we will call radial function-based regression (RfR) method. The RfR method employs a regression using Gaussian radial basis functions together with polynomial terms to facilitate the robust modeling of chaotic behavior. In this paper, we apply the RfR method to several types of relatively high-dimensional deterministic time series generated by a partial differential equation, a delay differential equation, a turbulence model, and intermittent dynamics. The case when the observation includes noise is also tested. We have effectively constructed a system of differential equations for each of these examples, which is assessed from the point of view of time series forecast, reconstruction of invariant sets, and invariant densities. We find that in some of the models, an appropriate trajectory is realized on the chaotic saddle and is identified by the Stagger-and-Step method.