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On the Use of Interval Extensions to Estimate the Largest Lyapunov Exponent from Chaotic Data
Joint Authors
Lacerda, Márcio J.
Nepomuceno, Erivelton G.
Martins, Samir A. M.
Mendes, Eduardo M. A. M.
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-03-04
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
A method to estimate the (positive) largest Lyapunov exponent (LLE) from data using interval extensions is proposed.
The method differs from the ones available in the literature in its simplicity since it is only based on three rather simple steps.
Firstly, a polynomial NARMAX is used to identify a model from the data under investigation.
Secondly, interval extensions, which can be easily extracted from the identified model, are used to calculate the lower bound error.
Finally, a simple linear fit to the logarithm of lower bound error is obtained and then the LLE is retrieved from it as the third step.
To illustrate the proposed method, the LLE is calculated for the following well-known benchmarks: sine map, Rössler Equations, and Mackey-Glass Equations from identified models given in the literature and also from two identified NARMAX models: a chaotic jerk circuit and the tent map.
In the latter, a Gaussian noise has been added to show the robustness of the proposed method.
American Psychological Association (APA)
Nepomuceno, Erivelton G.& Martins, Samir A. M.& Lacerda, Márcio J.& Mendes, Eduardo M. A. M.. 2018. On the Use of Interval Extensions to Estimate the Largest Lyapunov Exponent from Chaotic Data. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1208597
Modern Language Association (MLA)
Nepomuceno, Erivelton G.…[et al.]. On the Use of Interval Extensions to Estimate the Largest Lyapunov Exponent from Chaotic Data. Mathematical Problems in Engineering No. 2018 (2018), pp.1-8.
https://search.emarefa.net/detail/BIM-1208597
American Medical Association (AMA)
Nepomuceno, Erivelton G.& Martins, Samir A. M.& Lacerda, Márcio J.& Mendes, Eduardo M. A. M.. On the Use of Interval Extensions to Estimate the Largest Lyapunov Exponent from Chaotic Data. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1208597
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1208597