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
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
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.
Received: 26 March 2003
Revised: 18 May 2003
Accepted manuscript online:
Liu Wei-Dong (刘卫东), K. F. Ren, S. Meunier-Guttin-Cluzel, G. Gouesbet Global vector-field reconstruction of nonlinear dynamical systems from a time series with SVD method and validation with Lyapunov exponents 2003 Chinese Physics 12 1366
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