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dc.contributor.authorDanca, Marius-F.
dc.contributor.authorKuznetsov, Nikolay
dc.contributor.authorChen, Guanrong
dc.date.accessioned2018-01-29T09:26:31Z
dc.date.available2019-02-03T22:35:18Z
dc.date.issued2018
dc.identifier.citationDanca, Marius-F., Kuznetsov, N., & Chen, G. (2018). Approximating hidden chaotic attractors via parameter switching. <i>Chaos</i>, <i>28</i>(1), Article 013127. <a href="https://doi.org/10.1063/1.5007925" target="_blank">https://doi.org/10.1063/1.5007925</a>
dc.identifier.otherCONVID_27875302
dc.identifier.otherTUTKAID_76668
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/56933
dc.description.abstractIn this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical approximations of the underlying ω-limit sets (see, e.g., Ref. 31) after neglecting sufficiently long transients, can be numerically approximated by switching the control parameter in some deterministic or random manner, while the underlying initial value problem (IVP) is numerically integrated with the parameter switching (PS) algorithm. The attractors, whose basins of attractions are not connected with equilibria, are called hidden attractors, while the attractors for which the trajectories starting from a point in a neighborhood of an unstable equilibrium are attracted by some attractor are called self-excited attractors.4–6 In this paper, we prove analytically and verified numerically that the PS algorithm can be used to approximate any desired hidden attractors of a class of general systems, which model systems such as Lorenz, Chen, and Rössler.
dc.language.isoeng
dc.publisherAmerican Institute of Physics
dc.relation.ispartofseriesChaos
dc.subject.otherchaotic
dc.subject.othernonlinear systems
dc.subject.otherphase space methods
dc.subject.othernumerical approximations
dc.subject.otherchaotic systems
dc.titleApproximating hidden chaotic attractors via parameter switching
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201801261341
dc.contributor.laitosInformaatioteknologian tiedekuntafi
dc.contributor.laitosFaculty of Information Technologyen
dc.contributor.oppiaineTietotekniikkafi
dc.contributor.oppiaineMathematical Information Technologyen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2018-01-26T13:15:05Z
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.relation.issn1054-1500
dc.relation.numberinseries1
dc.relation.volume28
dc.type.versionpublishedVersion
dc.rights.copyright© American Institute of Physics, 2018. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.subject.ysokaaos
dc.subject.ysonumeerinen analyysi
dc.subject.ysodifferentiaalilaskenta
jyx.subject.urihttp://www.yso.fi/onto/yso/p13996
jyx.subject.urihttp://www.yso.fi/onto/yso/p15833
jyx.subject.urihttp://www.yso.fi/onto/yso/p7856
dc.relation.doi10.1063/1.5007925
dc.type.okmA1


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