Peixoto, Márcia L.C. and Nepomuceno, Erivelton and Martins, Samir A.M. and Lacerda, Márcio J. (2018) Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm. Chaos, Solitons & Fractals, 112. pp. 36-43. ISSN 09600779

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Abstract

It has been shown that natural interval extensions (NIE) can be used to calculate the largest positive Lyapunov exponent (LLE). However, the elaboration of NIE are not always possible for some dynamical systems, such as those modelled by simple equations or by Simulink-type blocks. In this paper, we use rounding mode of floating-point numbers to compute the LLE. We have exhibited how to produce two pseudo-orbits by means of different rounding modes; these pseudo-orbits are used to calculate the Lower Bound Error (LBE). The LLE is the slope of the line gotten from the logarithm of the LBE, which is estimated by means of a recursive least square algorithm (RLS). The main contribution of this paper is to develop a procedure to compute the LLE based on the LBE without using the NIE. Additionally, with the aid of RLS the number of required points has been decreased. Eight numerical examples are given to show the effectiveness of the proposed technique.

Item Type:	Article
Keywords:	Dynamical systems; Lyapunov exponent; Rounding mode; Lower bound error; Chaos; Recursive least square algorithm;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	16755
Identification Number:	https://doi.org/10.1016/j.chaos.2018.04.032
Depositing User:	Erivelton Nepomuceno
Date Deposited:	28 Nov 2022 16:16
Journal or Publication Title:	Chaos, Solitons & Fractals
Publisher:	Elsevier
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

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