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dc.contributor.authorKuznetsov, N. V.
dc.contributor.authorMokaev, T. N.
dc.contributor.authorKuznetsova, O. A.
dc.contributor.authorKudryashova, E. V.
dc.date.accessioned2020-08-17T11:49:28Z
dc.date.available2020-08-17T11:49:28Z
dc.date.issued2020
dc.identifier.citationKuznetsov, N. V., Mokaev, T. N., Kuznetsova, O. A., & Kudryashova, E. V. (2020). The Lorenz system : hidden boundary of practical stability and the Lyapunov dimension. <i>Nonlinear Dynamics</i>, <i>102</i>(2), 713-732. <a href="https://doi.org/10.1007/s11071-020-05856-4" target="_blank">https://doi.org/10.1007/s11071-020-05856-4</a>
dc.identifier.otherCONVID_41733182
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/71406
dc.description.abstractOn the example of the famous Lorenz system, the difficulties and opportunities of reliable numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz system, the boundaries of global stability are estimated and the difficulties of numerically studying the birth of self-excited and hidden attractors, caused by the loss of global stability, are discussed. The problem of reliable numerical computation of the finite-time Lyapunov dimension along the trajectories over large time intervals is discussed. Estimating the Lyapunov dimension of attractors via the Pyragas time-delayed feedback control technique and the Leonov method is demonstrated. Taking into account the problems of reliable numerical experiments in the context of the shadowing and hyperbolicity theories, experiments are carried out on small time intervals and for trajectories on a grid of initial points in the attractor’s basin of attraction.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofseriesNonlinear Dynamics
dc.rightsCC BY 4.0
dc.subject.otherglobal stability
dc.subject.otherchaos
dc.subject.otherhidden attractor
dc.subject.othertransient set
dc.subject.otherLyapunov exponents
dc.subject.otherLyapunov dimension
dc.subject.otherunstable periodic orbit
dc.subject.othertime-delayed feedback control
dc.titleThe Lorenz system : hidden boundary of practical stability and the Lyapunov dimension
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202008175542
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.description.reviewstatuspeerReviewed
dc.format.pagerange713-732
dc.relation.issn0924-090X
dc.relation.numberinseries2
dc.relation.volume102
dc.type.versionpublishedVersion
dc.rights.copyright© 2020 the Authors
dc.rights.accesslevelopenAccessfi
dc.subject.ysoattraktorit
dc.subject.ysokaaosteoria
dc.subject.ysosäätöteoria
dc.subject.ysonumeerinen analyysi
dc.subject.ysodynaamiset systeemit
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p38900
jyx.subject.urihttp://www.yso.fi/onto/yso/p6339
jyx.subject.urihttp://www.yso.fi/onto/yso/p868
jyx.subject.urihttp://www.yso.fi/onto/yso/p15833
jyx.subject.urihttp://www.yso.fi/onto/yso/p38899
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1007/s11071-020-05856-4
jyx.fundinginformationOpen access funding provided by University of Jyväskylä (JYU). This study was partially funded by the Russian Science Foundation (Project 19-41-02002).


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