Wavelet reconstruction of nonlinear dynamics

被引：22

作者：

Allingham, D ^{[1
]}

West, M ^{[1
]}

Mees, AI ^{[1
]}

机构：

[1] Univ Western Australia, Dept Math, Ctr Appl Dynam & Optimizat, Nedlands, WA 6907, Australia

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 1998年 / 8卷 / 11期

关键词：

D O I：

10.1142/S0218127498001789

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the reconstruction of embedded time-series from chaotic dynamical systems using wavelets. The standard wavelet transforms are not applicable because of the embedding, and we use a basis pursuit method which on its own does not perform very well. When this is combined with a continuous optimizer, however, we obtain very good models. We discuss the success of this method and apply it to some data from a vibrating string experiment.

引用

页码：2191 / 2201

页数：11

共 15 条

[1] Predicting chaotic time series with wavelet networks [J].

1600, Elsevier Science B.V., Amsterdam, Netherlands (85) :1-2

[2]

CHEN SS, 1996, UNPUB ATOMIC DECOMPO

[3]

DAUBECHIES I, 1992, LECT WAVELETS

[4]

DONOHO DL, 1992, UNCONDITIONAL BASES

[5]

GLENDENNING PA, 1983, J STAT PHYS, V35, P645

[6]

GLENDINNING P, 1983, 16 INT C THEOR APPL

[7] Modeling chaotic motions of a string from experimental data [J].

Judd, K ;

Mees, A .

PHYSICA D, 1996, 92 (3-4) :221-236

[8] ON SELECTING MODELS FOR NONLINEAR TIME-SERIES [J].

JUDD, K ;

MEES, A .

PHYSICA D, 1995, 82 (04) :426-444

[9] MATCHING PURSUITS WITH TIME-FREQUENCY DICTIONARIES [J].

MALLAT, SG ;

ZHANG, ZF .

IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1993, 41 (12) :3397-3415

[10] AN ALGORITHM FOR LEAST-SQUARES ESTIMATION OF NONLINEAR PARAMETERS [J].

MARQUARDT, DW .

JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1963, 11 (02) :431-441

← 1 2 →