{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T16:34:19Z","timestamp":1787243659017,"version":"3.56.0"},"reference-count":55,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["J4-9302"],"award-info":[{"award-number":["J4-9302"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["J1-9112"],"award-info":[{"award-number":["J1-9112"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["P1-0403"],"award-info":[{"award-number":["P1-0403"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2019,7]]},"abstract":"<jats:p>Soft computing strategies are drawing widespread interest in engineering and science fields, particularly so because of their capacity to reason and learn in a domain of inherent uncertainty, approximation, and unpredictability. However, soft computing research devoted to finite precision effects in chaotic system simulations is still in a nascent stage, and there are ample opportunities for new discoveries. In this paper, we consider the error that is due to finite precision in the simulation of chaotic systems. We present a generalized version of the lower bound error using an arbitrary number of natural interval extensions. The lower bound error has been used to simulate a chaotic system with lower and upper bounds. The width of this interval does not diverge, which is an advantage compared to other techniques. We illustrate our approach on three systems, namely the logistic map, the Singer map and the Chua circuit. Moreover, we validate the method by calculating the largest Lyapunov exponent.<\/jats:p>","DOI":"10.1142\/s0218127419501128","type":"journal-article","created":{"date-parts":[[2019,8,1]],"date-time":"2019-08-01T05:00:57Z","timestamp":1564635657000},"page":"1950112","source":"Crossref","is-referenced-by-count":11,"title":["Soft Computing Simulations of Chaotic Systems"],"prefix":"10.1142","volume":"29","author":[{"given":"Erivelton G.","family":"Nepomuceno","sequence":"first","affiliation":[{"name":"Control and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of S\u00e3o Jo\u00e3o del-Rei, S\u00e3o Jo\u00e3o del-Rei, MG 36307-352, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Priscila F. S.","family":"Guedes","sequence":"additional","affiliation":[{"name":"Control and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of S\u00e3o Jo\u00e3o del-Rei, S\u00e3o Jo\u00e3o del-Rei, MG 36307-352, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Al\u00edpio M.","family":"Barbosa","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Centro Universit\u00e1rio Newton Paiva, Belo Horizonte, MG 30431-189, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3087-541X","authenticated-orcid":false,"given":"Matja\u017e","family":"Perc","sequence":"additional","affiliation":[{"name":"Faculty of Natural Sciences and Mathematics, University of Maribor, Koro\u0161ka cesta 160, SI-2000 Maribor, Slovenia"},{"name":"CAMTP \u2014 Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia"},{"name":"Complexity Science Hub Vienna, Josefst\u00e4dterstra\u00dfe 39, A-1080 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert","family":"Repnik","sequence":"additional","affiliation":[{"name":"Faculty of Natural Sciences and Mathematics, University of Maribor, Koro\u0161ka cesta 160, SI-2000 Maribor, Slovenia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2019,8]]},"reference":[{"key":"S0218127419501128BIB001","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6645"},{"key":"S0218127419501128BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2009.03.196"},{"key":"S0218127419501128BIB003","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.3728"},{"key":"S0218127419501128BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s005000050002"},{"key":"S0218127419501128BIB005","doi-asserted-by":"publisher","DOI":"10.1109\/EIConRusNW.2015.7102231"},{"key":"S0218127419501128BIB006","doi-asserted-by":"publisher","DOI":"10.1080\/02286203.2008.11442464"},{"key":"S0218127419501128BIB007","doi-asserted-by":"publisher","DOI":"10.1109\/SSCI.2015.95"},{"key":"S0218127419501128BIB008","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/24\/10\/100501"},{"key":"S0218127419501128BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-92203-2_4"},{"key":"S0218127419501128BIB010","first-page":"250","volume":"46","author":"Chua L. O.","year":"1992","journal-title":"Int. J. Electron. Commun."},{"key":"S0218127419501128BIB011","doi-asserted-by":"publisher","DOI":"10.1109\/81.246149"},{"key":"S0218127419501128BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.01.028"},{"key":"S0218127419501128BIB013","doi-asserted-by":"publisher","DOI":"10.1109\/5.949483"},{"key":"S0218127419501128BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s11042-016-3907-z"},{"key":"S0218127419501128BIB016","volume-title":"The Topology of Chaos: Alice in Stretch and Squeezeland","author":"Gilmore R.","year":"2012"},{"key":"S0218127419501128BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/0885-064X(87)90024-0"},{"key":"S0218127419501128BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2013.10.031"},{"key":"S0218127419501128BIB019","doi-asserted-by":"publisher","DOI":"10.1109\/SCM.2015.7190417"},{"key":"S0218127419501128BIB020","doi-asserted-by":"publisher","DOI":"10.1109\/IECON.2000.972549"},{"key":"S0218127419501128BIB022","doi-asserted-by":"publisher","DOI":"10.4018\/978-1-4666-2518-1.ch002"},{"key":"S0218127419501128BIB023","doi-asserted-by":"publisher","DOI":"10.1088\/0143-0807\/26\/1\/021"},{"key":"S0218127419501128BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2014.08.034"},{"key":"S0218127419501128BIB025","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/978-981-10-3153-3_40","volume":"515","author":"Kumar R.","year":"2017","journal-title":"Adv. Intell. Syst. Comput."},{"key":"S0218127419501128BIB026","doi-asserted-by":"publisher","DOI":"10.1109\/CESYS.2017.8321190"},{"key":"S0218127419501128BIB027","first-page":"397","volume":"43","author":"Kurczyk S.","year":"2018","journal-title":"Arch. Acoust."},{"key":"S0218127419501128BIB028","volume-title":"Explorations in Numerical Analysis","author":"Lambers J. V.","year":"2016"},{"key":"S0218127419501128BIB030","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405014052"},{"key":"S0218127419501128BIB031","first-page":"015","volume":"32","author":"Liu L.","year":"2014","journal-title":"IMA J. Math. Contr. Inf."},{"key":"S0218127419501128BIB032","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2017.02.031"},{"key":"S0218127419501128BIB033","first-page":"1750103-1","volume":"27","author":"Liu L.","year":"2017","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"S0218127419501128BIB034","doi-asserted-by":"publisher","DOI":"10.1142\/9789814434867_0004"},{"key":"S0218127419501128BIB035","doi-asserted-by":"publisher","DOI":"10.1080\/10798587.2007.10642969"},{"key":"S0218127419501128BIB036","doi-asserted-by":"publisher","DOI":"10.1038\/261459a0"},{"key":"S0218127419501128BIB037","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416502266"},{"key":"S0218127419501128BIB038","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127415501242"},{"key":"S0218127419501128BIB039","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717716"},{"key":"S0218127419501128BIB040","first-page":"2","volume":"327","author":"Nepomuceno E. G.","year":"2014","journal-title":"J. Eng."},{"key":"S0218127419501128BIB041","doi-asserted-by":"publisher","DOI":"10.1080\/21642583.2016.1163296"},{"key":"S0218127419501128BIB042","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2016.12.002"},{"key":"S0218127419501128BIB043","doi-asserted-by":"publisher","DOI":"10.1080\/21642583.2017.1387874"},{"key":"S0218127419501128BIB044","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.02.020"},{"key":"S0218127419501128BIB045","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127418500554"},{"key":"S0218127419501128BIB046","doi-asserted-by":"publisher","DOI":"10.1080\/10739140802151846"},{"key":"S0218127419501128BIB047","volume-title":"Computer Arithmetic Algorithms and Hardware Architectures","author":"Parhami B.","year":"2012"},{"key":"S0218127419501128BIB048","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1987.13851"},{"key":"S0218127419501128BIB049","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-32613-8"},{"key":"S0218127419501128BIB050","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90009-P"},{"key":"S0218127419501128BIB051","first-page":"11","volume":"34","author":"\u0160alamon M.","year":"2004","journal-title":"Informacije MIDEM"},{"key":"S0218127419501128BIB052","first-page":"11","volume":"2","author":"Sarkar A.","year":"2014","journal-title":"Int. J. Amb. Syst. Appl."},{"key":"S0218127419501128BIB053","series-title":"Winter Simulation Conference","first-page":"9","volume-title":"Proc. 76 Bicentennial Conf. Winter Simulation, WSC\u201976","author":"Shannon R. E.","year":"1976"},{"key":"S0218127419501128BIB054","first-page":"40","volume":"10","author":"Sozhamadevi N.","year":"2015","journal-title":"Int. J. Appl. Eng. Res."},{"key":"S0218127419501128BIB055","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2009.12.011"},{"key":"S0218127419501128BIB056","doi-asserted-by":"publisher","DOI":"10.1109\/GRC.2008.4664777"},{"key":"S0218127419501128BIB057","doi-asserted-by":"crossref","first-page":"109","DOI":"10.15388\/NA.2010.15.1.14368","volume":"15","author":"Yao L.-S.","year":"2010","journal-title":"Nonlin. Anal.: Model. Contr."},{"key":"S0218127419501128BIB058","doi-asserted-by":"publisher","DOI":"10.1109\/52.329401"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127419501128","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T15:12:48Z","timestamp":1695049968000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127419501128"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7]]},"references-count":55,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2019,8]]},"published-print":{"date-parts":[[2019,7]]}},"alternative-id":["10.1142\/S0218127419501128"],"URL":"https:\/\/doi.org\/10.1142\/s0218127419501128","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7]]}}}