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Article: An improvement on Marotto's theorem and its applications to chaotification of switching systems

TitleAn improvement on Marotto's theorem and its applications to chaotification of switching systems
Authors
Zhao, YXie, LYiu, KFC
Issue Date2009
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/chaos
Citation
Chaos, Solitons And Fractals, 2009, v. 39 n. 5, p. 2225-2232 How to Cite?
DOI: http://dx.doi.org/10.1016/j.chaos.2007.06.109
AbstractThe controversy surrounding the correctness of Marotto's theorem continues over the last two decades, with many researchers claiming to have found an error in the proof. In this paper, we show that Marotto's theorem is indeed correct for analyzing the existence of chaos in the sense of Li-Yorke even after relaxing certain assumptions in the proof. In addition, we extend the theory to derive the conditions for the existence of chaos in the sense of Devaney. We show that these results can be applied to study the chaotification of linear switching systems. © 2007 Elsevier Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/155916
ISSN
0960-0779
2021 Impact Factor: 9.922
2020 SCImago Journal Rankings: 1.043
ISI Accession Number ID
WOS:000265891700024
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorZhao, Yen_US
dc.contributor.authorXie, Len_US
dc.contributor.authorYiu, KFCen_US
dc.date.accessioned2012-08-08T08:38:23Z-
dc.date.available2012-08-08T08:38:23Z-
dc.date.issued2009en_US
dc.identifier.citationChaos, Solitons And Fractals, 2009, v. 39 n. 5, p. 2225-2232en_US
dc.identifier.issn0960-0779en_US
dc.identifier.urihttp://hdl.handle.net/10722/155916-
dc.description.abstractThe controversy surrounding the correctness of Marotto's theorem continues over the last two decades, with many researchers claiming to have found an error in the proof. In this paper, we show that Marotto's theorem is indeed correct for analyzing the existence of chaos in the sense of Li-Yorke even after relaxing certain assumptions in the proof. In addition, we extend the theory to derive the conditions for the existence of chaos in the sense of Devaney. We show that these results can be applied to study the chaotification of linear switching systems. © 2007 Elsevier Ltd. All rights reserved.en_US
dc.languageengen_US
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/chaosen_US
dc.relation.ispartofChaos, Solitons and Fractalsen_US
dc.titleAn improvement on Marotto's theorem and its applications to chaotification of switching systemsen_US
dc.typeArticleen_US
dc.identifier.emailYiu, KFC:cedric@hkucc.hku.hken_US
dc.identifier.authorityYiu, KFC=rp00206en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.chaos.2007.06.109en_US
dc.identifier.scopuseid_2-s2.0-64049119206en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-64049119206&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume39en_US
dc.identifier.issue5en_US
dc.identifier.spage2225en_US
dc.identifier.epage2232en_US
dc.identifier.isiWOS:000265891700024-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridZhao, Y=8713567900en_US
dc.identifier.scopusauthoridXie, L=8649291500en_US
dc.identifier.scopusauthoridYiu, KFC=24802813000en_US
dc.identifier.issnl0960-0779-

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