Global vector-field reconstruction of nonlinear dynamical systems from a time series with SVD method and validation with Lyapunov exponents

• 来源期刊: 中国物理（英文版）
• 关键词: global vector-field reconstruction Lyapunov exponents model validation
• 年，卷（期）: 2003,（12）
• 页码范围: 1366-1373
• 页数: 8页
• 语种: 英文

摘要

A method for the global vector-field reconstruction of nonlinear dynamical systems from a time series is studied in this paper. It employs a complete set of polynomials and singular value decomposition (SVD) to estimate a standard function which is central to the algorithm. Lyapunov exponents and dimension, calculated from the differential equations of a standard system, are used for the validation of the reconstruction. The algorithm is proven to be practical by applying it to a Rossler system.