Nepomuceno, Erivelton and Rodrigues Junior, Heitor M. and Martins, Samir A.M. and Perc, Matjaž and Slavinec, Mitja (2018) Interval computing periodic orbits of maps using a piecewise approach. Applied Mathematics and Computation, 336. pp. 67-75. ISSN 00963003

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Abstract

Interval arithmetic applied to simulation of dynamical systems has attracted a great deal of interest in recent years. Much of this research has been carried out in the calculation of fixed points or low-period windows for nonlinear discrete maps. This study proposes a novel interval computation based on a piecewise method to calculate periodic orbits for the logistic map. Using the cobweb plot, three rounding situations have been applied to a correct outward rounding, as required by interval arithmetic. The proposed method is compared with results in the literature and with the results obtained by means of the Matlab toolbox Intlab. The comparison is accomplished for nine case studies using the logistic map. Numerical results explicitly indicate that the proposed method produces intervals that are substantially narrower than those obtained with the traditional techniques.

Item Type:	Article
Keywords:	Interval arithmetic; periodic orbit; Natural interval extensions; Discrete maps; Dynamical systems;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	16752
Identification Number:	https://doi.org/10.1016/j.amc.2018.04.063
Depositing User:	Erivelton Nepomuceno
Date Deposited:	28 Nov 2022 15:49
Journal or Publication Title:	Applied Mathematics and Computation
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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