Singular-value decomposition in attractor reconstruction: Pitfalls and precautions

DOI10.1016/0167-2789(92)90198-VzbMath0744.58046OpenAlexW2072409296MaRDI QIDQ1184314

Ivan Dvořák, Milan Paluš

Publication date: 28 June 1992

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(92)90198-v

zbMATH Keywords

singular-value decompositionstrange attractorembedding dimensionone-dimensional chaotic time series

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Ergodic theory (37A99)

Related Items (15)

Phase portrait reconstruction using multivariate singular systems analysis ⋮ Estimating the correlation dimension of an attractor from noisy and small datasets based on re-embedding ⋮ Application of the correlation integral to respiratory data of infants during REM sleep ⋮ Experimental nonlinear physics ⋮ Indications of nonlinearity, intraindividual specificity and stability of human EEG: The unfolding dimension ⋮ Significance testing of information theoretic functionals ⋮ The analysis of chaotic time-series data ⋮ Estimating the errors on measured entropy and mutual information ⋮ Identification determinism in time series based on symplectic geometry spectra ⋮ A discrete mathematical model for chaotic dynamics in economics: Kaldor's model on business cycle ⋮ A new adaptive local linear prediction method and its application in hydrological time series ⋮ On the detection of determinism in a time series ⋮ LOCAL ANALYSIS OF DISSIPATIVE DYNAMICAL SYSTEMS ⋮ A method of embedding dimension estimation based on symplectic geometry ⋮ Kaldor-Kalecki new model on business cycles

Cites Work

• Stochastic phenomena and chaotic behaviour in complex systems. Proceedings of the Fourth Meeting of the UNESCO Working Group on Systems Analysis, Flattnitz, Kärnten, Austria, June 6-10, 1983
• Reconstructing attractors from scalar time series: A comparison of singular system and redundancy criteria
• A two-dimensional mapping with a strange attractor
• Dimensions and entropies in chaotic systems. Quantification of complex behavior. Proceedings of an International Workshop at the Pecos River Ranch, New Mexico, September 11-16, 1985
• Dimensions and entropies of strange attractors from a fluctuating dynamics approach
• Chaotic phenomena
• Measuring the strangeness of strange attractors
• Extracting qualitative dynamics from experimental data
• Information and entropy in strange attractors
• Independent coordinates for strange attractors from mutual information
• Topological dimension and local coordinates from time series data
• Deterministic Nonperiodic Flow
• An Algorithm for Finding Intrinsic Dimensionality of Data
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Singular-value decomposition in attractor reconstruction: Pitfalls and precautions