Global vector-field reconstruction of nonlinear dynamical systems from a time series with SVD method and validation with Lyapunov exponents
基于SVD方法的非线性动力系统全局矢量场重构及Lyapunov指数验证作者机构:DepartmentofAerospaceTechnologyNatlonalUniversityofDefenseTechnologyChangsha410073China L.E.S.P.U.M.R.6614INSAdeRouen76801SaintEtienneduRouvrayFrance
出 版 物:《Chinese Physics B》 (中国物理B(英文版))
年 卷 期:2003年第12卷第12期
页 面:1366-1373页
核心收录:
学科分类:07[理学] 070104[理学-应用数学] 0701[理学-数学]
主 题:global vector-field reconstruction Lyapunov exponents model validation
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.