Estimating the lyapunov exponents of chaotic time series based on polynomial modelling

M. Ataei; A. Khaki-Sedigh; B. Lohmann

doi:10.1016/S1474-6670(17)34757-2

Estimating the lyapunov exponents of chaotic time series based on polynomial modelling

M. Ataei, A. Khaki-Sedigh, B. Lohmann

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

The problem of Lyapunov Exponents (LEs) estimation from chaotic data based on Jacobian approach by polynomial models is considered. The optimum embedding dimension of reconstructed attractor is interpreted as suitable order of model. Therefore, based on global polynomial mode ling of system, a novel criterion for selecting the embedding dimension is presented. By considering this dimension as the model order, the best nonlinearity degree of polynomial is estimated. The selected structure is used for local estimating of Jacobians to calculate the LEs. This suitable structure of polynomial model leads to better results and avoids of sporious LEs. Simulation results show the effectiveness of proposed methodology.

Original language	English
Pages (from-to)	169-174
Number of pages	6
Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	36
Issue number	16
DOIs	https://doi.org/10.1016/S1474-6670(17)34757-2
State	Published - 2003
Externally published	Yes
Event	13th IFAC Symposium on System Identification, SYSID 2003 - Rotterdam, Netherlands Duration: 27 Aug 2003 → 29 Aug 2003

Keywords

Chaos
Jacobian matrices
Lyapunov exponents
factorization
polynomial models
time series

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10.1016/S1474-6670(17)34757-2

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title = "Estimating the lyapunov exponents of chaotic time series based on polynomial modelling",

abstract = "The problem of Lyapunov Exponents (LEs) estimation from chaotic data based on Jacobian approach by polynomial models is considered. The optimum embedding dimension of reconstructed attractor is interpreted as suitable order of model. Therefore, based on global polynomial mode ling of system, a novel criterion for selecting the embedding dimension is presented. By considering this dimension as the model order, the best nonlinearity degree of polynomial is estimated. The selected structure is used for local estimating of Jacobians to calculate the LEs. This suitable structure of polynomial model leads to better results and avoids of sporious LEs. Simulation results show the effectiveness of proposed methodology.",

keywords = "Chaos, Jacobian matrices, Lyapunov exponents, factorization, polynomial models, time series",

author = "M. Ataei and A. Khaki-Sedigh and B. Lohmann",

note = "Publisher Copyright: {\textcopyright} 2003 International Federation of Automatic Control.; 13th IFAC Symposium on System Identification, SYSID 2003 ; Conference date: 27-08-2003 Through 29-08-2003",

year = "2003",

doi = "10.1016/S1474-6670(17)34757-2",

language = "English",

volume = "36",

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journal = "IFAC Proceedings Volumes (IFAC-PapersOnline)",

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TY - JOUR

T1 - Estimating the lyapunov exponents of chaotic time series based on polynomial modelling

AU - Ataei, M.

AU - Khaki-Sedigh, A.

AU - Lohmann, B.

PY - 2003

Y1 - 2003

N2 - The problem of Lyapunov Exponents (LEs) estimation from chaotic data based on Jacobian approach by polynomial models is considered. The optimum embedding dimension of reconstructed attractor is interpreted as suitable order of model. Therefore, based on global polynomial mode ling of system, a novel criterion for selecting the embedding dimension is presented. By considering this dimension as the model order, the best nonlinearity degree of polynomial is estimated. The selected structure is used for local estimating of Jacobians to calculate the LEs. This suitable structure of polynomial model leads to better results and avoids of sporious LEs. Simulation results show the effectiveness of proposed methodology.

AB - The problem of Lyapunov Exponents (LEs) estimation from chaotic data based on Jacobian approach by polynomial models is considered. The optimum embedding dimension of reconstructed attractor is interpreted as suitable order of model. Therefore, based on global polynomial mode ling of system, a novel criterion for selecting the embedding dimension is presented. By considering this dimension as the model order, the best nonlinearity degree of polynomial is estimated. The selected structure is used for local estimating of Jacobians to calculate the LEs. This suitable structure of polynomial model leads to better results and avoids of sporious LEs. Simulation results show the effectiveness of proposed methodology.

KW - Chaos

KW - Jacobian matrices

KW - Lyapunov exponents

KW - factorization

KW - polynomial models

KW - time series

UR - http://www.scopus.com/inward/record.url?scp=85018263971&partnerID=8YFLogxK

U2 - 10.1016/S1474-6670(17)34757-2

DO - 10.1016/S1474-6670(17)34757-2

M3 - Conference article

AN - SCOPUS:85018263971

SN - 1474-6670

VL - 36

SP - 169

EP - 174

JO - IFAC Proceedings Volumes (IFAC-PapersOnline)

JF - IFAC Proceedings Volumes (IFAC-PapersOnline)

IS - 16

T2 - 13th IFAC Symposium on System Identification, SYSID 2003

Y2 - 27 August 2003 through 29 August 2003

ER -

Estimating the lyapunov exponents of chaotic time series based on polynomial modelling

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