Please use this identifier to cite or link to this item:
http://hdl.handle.net/1843/57005
Type: | Artigo de Periódico |
Title: | On the use of interval extensions to estimate the largest lyapunov exponent from chaotic data |
Authors: | Erivelton Geraldo Nepomuceno Samir Martins Márcio Lacerda Eduardo Mazoni Andrade Marçal Mendes |
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. |
Subject: | Liapunov, Funções de |
language: | por |
metadata.dc.publisher.country: | Brasil |
Publisher: | Universidade Federal de Minas Gerais |
Publisher Initials: | UFMG |
metadata.dc.publisher.department: | ENG - DEPARTAMENTO DE ENGENHARIA ELETRÔNICA |
Rights: | Acesso Aberto |
metadata.dc.identifier.doi: | https://doi.org/10.1155/2018/6909151 |
URI: | http://hdl.handle.net/1843/57005 |
Issue Date: | 2018 |
metadata.dc.url.externa: | https://www.hindawi.com/journals/mpe/2018/6909151/#copyright |
metadata.dc.relation.ispartof: | Mathematical problems in engineering |
Appears in Collections: | Artigo de Periódico |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
On the Use of Interval Extensions to Estimate the Largest Lyapunov Exponent from Chaotic Data.pdf | 5.35 MB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.