中国物理B ›› 2003, Vol. 12 ›› Issue (12): 1366-1373.doi: 10.1088/1009-1963/12/12/005

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

刘卫东1, K. F. Ren2, S. Meunier-Guttin-Cluzel2, G. Gouesbet2   

  1. (1)Department of Aerospace Technology, National University of Defense Technology, Changsha 410073, China; (2)L.E.S.P., U.M.R. 6614, INSA de Rouen, 76801, Saint Etienne du Rouvray, France
  • 收稿日期:2003-03-26 修回日期:2003-05-18 出版日期:2003-12-16 发布日期:2005-03-16

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

Liu Wei-Dong (刘卫东)a, K. F. Renb, S. Meunier-Guttin-Cluzelb, G. Gouesbetb   

  1. a Department of Aerospace Technology, National University of Defense Technology, Changsha 410073, China; b L.E.S.P., U.M.R. 6614, INSA de Rouen, 76801, Saint Etienne du Rouvray, France
  • Received:2003-03-26 Revised:2003-05-18 Online:2003-12-16 Published:2005-03-16

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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 R?ssler system.

Abstract: 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 R?ssler system.

Key words: global vector-field reconstruction, Lyapunov exponents, model validation

中图分类号:  (Time series analysis)

  • 05.45.Tp
02.30.Hq (Ordinary differential equations) 02.10.Yn (Matrix theory) 02.10.De (Algebraic structures and number theory)