Nepomuceno, Erivelton and Mendes, Eduardo M.A.M. (2017) On the analysis of pseudo-orbits of continuous chaotic nonlinear systems simulated using discretization schemes in a digital computer. Chaos, Solitons & Fractals, 95. pp. 21-32. ISSN 0960-0779

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Abstract

This paper reports the existence of more than one pseudo-orbit when simulating continuous nonlinear systems using a digital computer in a set-up different from the ones normally seen in the literature, that is, in a set-up where the step-size is not varied, the discretization scheme is kept the same as well as the initial conditions. Taking advantage of the roundoff error, a simple but effective method to determine a lower bound error and the critical time for the pseudo-orbits is used and the connection to the maximum (positive) Lyapunov exponent is established considering the bit resolution and the computational platform used for the simulations. To illustrate the effectiveness of the method and problems of using discretization schemes for simulating continuous nonlinear systems in a digital computer, the well-known Lorenz equations, the Rossler hyperchaos system, Mackey–Glass equation and the Sprott A system are used. The method can help the user of such schemes to keep track of the reliability of numerical simulations.

Item Type:	Article
Keywords:	Nonlinear dynamics systems; Chaos; Discretization schemes; Pseudo-Orbit; Lower bound error; Lyapunov exponent;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	16765
Identification Number:	https://doi.org/10.1016/j.chaos.2016.12.002
Depositing User:	Erivelton Nepomuceno
Date Deposited:	05 Dec 2022 17:02
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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