Modeling nonlinear dynamics and chaos: a review
type: Item
instance of: scholarly article
title: Modeling nonlinear dynamics and chaos: a review
zbMATH Open document ID: 1180.37003
DOI: 10.1155/2009/238960
author: C. Letellier
author: Luis Antonio Aguirre
published in: Mathematical Problems in Engineering
publication date: 2009-11-13T00:00:00Z
full work available at URL: https://eudml.org/doc/45811
review text: Summary: 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.
Mathematics Subject Classification ID: 37-02
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 5632453
zbMATH Keywords: parameter estimation technique
zbMATH Keywords: model validation
Wikidata QID: Q58648922
describes a project that uses: Sprott's Software
describes a project that uses: MOSSFARM
MaRDI profile type: Publication
OpenAlex ID: W2111480264
cites work: Q5582924
cites work: Deterministic Nonperiodic Flow
cites work: On the nature of turbulence
cites work: An equation for continuous chaos
cites work: Period Three Implies Chaos
cites work: Q3658782
cites work: Q3333765
cites work: State space reconstruction in the presence of noise
cites work: Embedology
cites work: Q5186444
cites work: Q3255653
cites work: Nonlinear Time Series Analysis
cites work: Q4862306
cites work: Q4263623
cites work: Optimal expansions of discrete-time Volterra models using Laguerre functions
cites work: Input-output parametric models for non-linear systems Part II: stochastic non-linear systems
cites work: Rational model identification using an extended least-squares algorithm
cites work: Predicting chaotic time series with wavelet networks
cites work: An extended orthogonal forward regression algorithm for system identification using entropy
cites work: An adaptive orthogonal search algorithm for model subset selection and non-linear system identification
cites work: Model selection approaches for non-linear system identification: a review
cites work: Q5505866
cites work: Q3830265
cites work: Q3805940
cites work: Nonlinear prediction of chaotic time series
cites work: Dynamics from multivariate time series
cites work: NONLINEAR TIME SEQUENCE ANALYSIS
cites work: Regularized local linear prediction of chaotic time series
cites work: Nonlinear deterministic forecasting of daily Peseta--Dollar exchange rate
cites work: Identification of pre-sliding friction dynamics
cites work: Construction of phenomenological models from numerical scalar time series
cites work: Structure-selection techniques applied to continuous-time nonlinear models
cites work: Determining mixed linear-nonlinear coupled differential equations from multivariate discrete time series sequences
cites work: Topological analysis of chaos in equivariant electronic circuits
cites work: Parametric, nonparametric and parametric modelling of a chaotic circuit time series
cites work: Dynamical modelling of measured time series from a Q-switched CO\(_{2}\) laser.
cites work: Using neural nets to look for chaos
cites work: Extraction of nonlinear dynamics from short and noisy time series
cites work: Q3375815
cites work: Identification and prediction of low dimensional dynamics
cites work: Time series analysis and prediction on complex dynamical behavior observed in a blast furnace
cites work: Modelling the dynamics of nonlinear time series using canonical variate analysis
cites work: Generalized one-parameter bifurcation diagram reconstruction using time series
cites work: Time series-based bifurcation diagram reconstruction
cites work: Detection of chaotic determinism in time series from randomly forced maps
cites work: Multivariate polynomial regression for identification of chaotic time series
cites work: The use of synthetic input sequences in time series modeling
cites work: Nonlinear interactions in a rotating disk flow: From a Volterra model to the Ginzburg-Landau equation
cites work: Investigation of determinism in heart rate variability
cites work: Identification of non-linear rational systems using a prediction-error estimation algorithm
cites work: Parameter estimation for stochastic nonlinear rational models
cites work: Wavelet Reconstruction of Nonlinear Dynamics
cites work: DISCRETE WAVELET MODELS FOR IDENTIFICATION AND QUALITATIVE ANALYSIS OF CHAOTIC SYSTEMS
cites work: Identification and reconstruction of chaotic systems using multiresolution wavelet decompositions
cites work: Q4467025
cites work: An adaptive fuzzy system for modeling chaos
cites work: Global vector field reconstruction including a control parameter dependence.
cites work: Input-output parametric models for non-linear systems Part I: deterministic non-linear systems
cites work: RETRIEVING DYNAMICAL INVARIANTS FROM CHAOTIC DATA USING NARMAX MODELS

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Reconstruction of the Lorenz and Chen systems with noisy observations

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Displacement in the parameter space versus spurious solution of discretization with large time step

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Discrete time recurrent neural network architectures: A unifying review

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Improving generalization of MLPs with multi-objective optimization

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Applying the method of surrogate data to cyclic time series

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Inverting chaos: Extracting system parameters from experimental data

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Global reconstruction in the presence of \textit{a priori} information

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Extraction of dynamical equations from chaotic data

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: PARSIMONIOUS DYNAMICAL RECONSTRUCTION

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: GLOBAL DYNAMICAL EQUATIONS AND LYAPUNOV EXPONENTS FROM NOISY CHAOTIC TIME SERIES

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Dynamical effects of overparametrization in nonlinear models

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: GLOBAL NONLINEAR POLYNOMIAL MODELS: STRUCTURE, TERM CLUSTERS AND FIXED POINTS

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: On Identifying Global Nonlinear Discrete Models from Chaotic Data

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: On Overparametrization of Nonlinear Discrete Systems

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: SOME REMARKS ON STRUCTURE SELECTION FOR NONLINEAR MODELS

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Improved structure selection for nonlinear models based on term clustering

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Parameter uncertainties in models of equivariant dynamical systems

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Q3995624

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: On selecting models for nonlinear time series

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Identification of MIMO non-linear systems using a forward-regression orthogonal estimator

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Identification of models for chaotic systems from noisy data: implications for performance and nonlinear filtering

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Investigating nonlinear dynamics from time series: The influence of symmetries and the choice of observables

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: How the choice of the observable may influence the analysis of nonlinear dynamical systems

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Quantitative Determination of Abrupt Changes in Dynamical Systems: Illustration Via Identification of Seizure Termination in Generalized Tonic–Clonic Seizure EEG Data

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Q4816378

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Embedding as a modeling problem

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Fitting model equations to time series using chaos synchronization

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Problems in estimating dynamics from data

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: NONLINEAR DYNAMICAL SYSTEM IDENTIFICATION FROM UNCERTAIN AND INDIRECT MEASUREMENTS

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Parameter identification in noisy extended systems: a hydrodynamic case

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: On the trajectory method for the reconstruction of differential equations from time series

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: A LEARNING ALGORITHM FOR OPTIMAL REPRESENTATION OF EXPERIMENTAL DATA

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Modeling Noisy Time Series: Physiological Tremor

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Reconstruction of time-delayed feedback systems from time series

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Estimation of parameters in one-dimensional maps from noisy chaotic time series

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: NONLINEAR IDENTIFICATION USING PRIOR KNOWLEDGE OF FIXED POINTS: A MULTIOBJECTIVE APPROACH

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: VALIDATING IDENTIFIED NONLINEAR MODELS WITH CHAOTIC DYNAMICS

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: INTEGRATING IDENTIFICATION AND QUALITATIVE ANALYSIS FOR THE DYNAMIC MODEL OF A LAGOON

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Identification of coupled map lattice models of complex spatio-temporal patterns

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: ANALYSIS OF A NONSYNCHRONIZED SINUSOIDALLY DRIVEN DYNAMICAL SYSTEM

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Comparisons of new nonlinear modeling techniques with applications to infant respiration.

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Testing for nonlinearity in time series: the method of surrogate data

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Consistent nonlinear dynamics: identifying model inadequacy

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Cost of synchronizing different chaotic systems

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: The Topology of Chaos

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: On the non-equivalence of observables in phase-space reconstructions from recorded time series

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Grey-box modelling and identification using physical knowledge and Bayesian techniques

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Identification of nonlinear systems using empirical data and prior knowledge -- An optimization approach

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Models of knowing and the investigation of dynamical systems

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Piecewise affine models of chaotic attractors: The Rössler and Lorenz systems

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: SUMMARY OF THE SECOND WORKSHOP ON MEASURES OF COMPLEXITY AND CHAOS

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Simple mathematical models with very complicated dynamics

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: A two-dimensional mapping with a strange attractor

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Identifying chaotic systems using Wiener and Hammerstein cascade models

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Oscillation and Chaos in Physiological Control Systems

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Detecting nonlinearity in multivariate time series

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Deterministic structure in multichannel physiological data

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: A General Form for Global Dynamical Data Models for Three-Dimensional Systems

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Global models from the Canadian lynx cycles as a direct evidence for chaos in real ecosystems

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: MUTUAL SYNCHRONIZATION OF CHAOTIC SELF-OSCILLATORS WITH DISSIPATIVE COUPLING

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: The double scroll

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Nonlinear Identification and Cluster Analysis of Chaotic Attractors from a Real Implementation of Chua's Circuit

Modeling nonlinear dynamics and chaos: a review (cites work)
cites work: Learning of Chua's circuit attractors by locally recurrent neural networks

Modeling nonlinear dynamics and chaos: a review (Recommended article)
Recommended article: Nonlinear dynamics and chaos. Advances and perspectives
Similarity Score: 0.91611016
Recommender Run: Recommender Run 3

Modeling nonlinear dynamics and chaos: a review (Recommended article)
Recommended article: Q4255451
Similarity Score: 0.90570974
Recommender Run: Recommender Run 3

Modeling nonlinear dynamics and chaos: a review (Recommended article)
Recommended article: Nonlinear dynamics and chaotic phenomena. An introduction
Similarity Score: 0.9046018
Recommender Run: Recommender Run 3

Modeling nonlinear dynamics and chaos: a review (Recommended article)
Recommended article: Nonlinear dynamics and chaotic phenomena. An introduction
Similarity Score: 0.9046018
Recommender Run: Recommender Run 3

Modeling nonlinear dynamics and chaos: a review (Recommended article)
Recommended article: Q3128839
Similarity Score: 0.9044925
Recommender Run: Recommender Run 3

Modeling nonlinear dynamics and chaos: a review (Recommended article)
Recommended article: Nonlinear dynamics and chaos
Similarity Score: 0.9022517
Recommender Run: Recommender Run 3

Modeling nonlinear dynamics and chaos: a review (Recommended article)
Recommended article: Nonlinear dynamics of chaotic and stochastic systems. Tutorial and modern developments
Similarity Score: 0.9020015
Recommender Run: Recommender Run 3

Modeling nonlinear dynamics and chaos: a review (Recommended article)
Recommended article: Nonlinear dynamics of chaotic and stochastic systems. Tutorial and modern developments
Similarity Score: 0.9020015
Recommender Run: Recommender Run 3

Modeling nonlinear dynamics and chaos: a review (Recommended article)
Recommended article: Q4003098
Similarity Score: 0.90039796
Recommender Run: Recommender Run 3