Nepomuceno, Erivelton and Martins, Samir A. M. and Lacerda, Márcio J. and 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, 2018. pp. 1-8. ISSN 1024-123X

Preview

Download (1MB) | Preview

Abstract

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.

Item Type:	Article
Keywords:	Interval Extensions; Estimate; Largest; Lyapunov Exponent; Chaotic Data;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	16757
Identification Number:	https://doi.org/10.1155/2018/6909151
Depositing User:	Erivelton Nepomuceno
Date Deposited:	29 Nov 2022 16:24
Journal or Publication Title:	Mathematical Problems in Engineering
Publisher:	Hindawi
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

Repository Staff Only(login required)

Item control page

Downloads

Origin of downloads