Modeling Nonlinear Dynamics and Chaos: A Review

被引：94

作者：

Aguirre, Luis A. ^{[1
]}

Letellier, Christophe ^{[2
]}

机构：

[1] Univ Fed Minas Gerais, Dept Engn Eletron UFMG, BR-31270901 Belo Horizonte, MG, Brazil

[2] Univ Rouen, CORIA, UMR 6614, F-76801 St Etienne, France

来源：

MATHEMATICAL PROBLEMS IN ENGINEERING | 2009年 / 2009卷

关键词：

VECTOR-FIELD RECONSTRUCTION; NON-LINEAR SYSTEMS; OUTPUT PARAMETRIC MODELS; TIME-SERIES ANALYSIS; STRUCTURE-SELECTION; DIFFERENTIAL-EQUATIONS; PRIOR KNOWLEDGE; NEURAL-NETWORK; TOPOLOGICAL CHARACTERIZATION; BIFURCATION DIAGRAMS;

D O I：

10.1155/2009/238960

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This paper reviews the major developments of modeling techniques applied to nonlinear dynamics and chaos. Model representations, parameter estimation techniques, data requirements, and model validation are some of the key topics that are covered in this paper, which surveys slightly over two decades since the pioneering papers on the subject appeared in the literature. Copyright (C) 2009 L. A. Aguirre and C. Letellier.

引用

页数：35

共 235 条

[1] THE ANALYSIS OF OBSERVED CHAOTIC DATA IN PHYSICAL SYSTEMS [J].

ABARBANEL, HDI ;

BROWN, R ;

SIDOROWICH, JJ ;

TSIMRING, LS .

REVIEWS OF MODERN PHYSICS, 1993, 65 (04) :1331-1392

[2] PREDICTION IN CHAOTIC NONLINEAR-SYSTEMS - METHODS FOR TIME-SERIES WITH BROAD-BAND FOURIER SPECTRA [J].

ABARBANEL, HDI ;

BROWN, R ;

KADTKE, JB .

PHYSICAL REVIEW A, 1990, 41 (04) :1782-1807

[3]

Adomaitis R. A., 1990, Neural Networks: Biological Computers or Electronic Brains, P87

[4]

Aguirre G., 1995, Veterinary & Comparative Ophthalmology, V5, P2

[5] Forecasting the time series of sunspot numbers [J].

Aguirre, L. A. ;

Letellier, C. ;

Maquet, J. .

SOLAR PHYSICS, 2008, 249 (01) :103-120

[6] Constraining the topology of neural networks to ensure dynamics with symmetry properties [J].

Aguirre, LA ;

Lopes, RAM ;

Amaral, GFV ;

Letellier, C .

PHYSICAL REVIEW E, 2004, 69 (02) :026701-1

[7] VALIDATING IDENTIFIED NONLINEAR MODELS WITH CHAOTIC DYNAMICS [J].

AGUIRRE, LA ;

BILLINGS, SA .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1994, 4 (01) :109-125

[8] Using data-driven discrete-time models and the unscented Kalman filter to estimate unobserved variables of nonlinear systems -: art. no. 026226 [J].

Aguirre, LA ;

Teixeira, BOS ;

Tôrres, LAB .

PHYSICAL REVIEW E, 2005, 72 (02)

[9] DYNAMICAL EFFECTS OF OVERPARAMETRIZATION IN NONLINEAR MODELS [J].

AGUIRRE, LA ;

BILLINGS, SA .

PHYSICA D, 1995, 80 (1-2) :26-40

[10] Nonlinear identification and cluster analysis of chaotic attractors from a real implementation of Chua's circuit [J].

Aguirre, LA ;

Rodrigues, GG ;

Mendes, EMAM .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1997, 7 (06) :1411-1423

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