Stabilization of cycles for difference equations with a noisy PF control

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dc.contributor.authorBraverman, Elenacs
dc.contributor.authorDiblík, Josefcs
dc.contributor.authorRodkina, Alexandracs
dc.contributor.authorŠmarda, Zdeněkcs
dc.coverage.issue1cs
dc.coverage.volume115cs
dc.date.accessioned2020-11-20T15:54:32Z
dc.date.available2020-11-20T15:54:32Z
dc.date.issued2020-02-21cs
dc.description.abstractDifference equations, such as a Ricker map, for an increased value of the parameter, experience instability of the positive equilibrium and transition to deterministic chaos. To achieve stabilization, various methods can be applied. Proportional Feedback control suggests a proportional reduction of the state variable at every kth step. First, if k not equal 1, a cycle is stabilized rather than an equilibrium. Second, the equation can incorporate an additive noise term, describing the variability of the environment, as well as multiplicative noise corresponding to possible deviations in the control intensity. The present paper deals with both issues, it justifies a possibility of getting a stable blurred k-cycle. Presented examples include the Ricker model, as well as equations with unbounded f, such as the bobwhite quail population models. Though the theoretical results justify stabilization for either multiplicative or additive noise only, numerical simulations illustrate that a blurred cycle can be stabilized when both multiplicative and additive noises are involved. (C) 2020 Elsevier Ltd. All rights reserved.en
dc.formattextcs
dc.format.extent1-8cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationAUTOMATICA. 2020, vol. 115, issue 1, p. 1-8.en
dc.identifier.doi10.1016/j.automatica.2020.108862cs
dc.identifier.issn0005-1098cs
dc.identifier.other163803cs
dc.identifier.urihttp://hdl.handle.net/11012/195668
dc.language.isoencs
dc.publisherElseviercs
dc.relation.ispartofAUTOMATICAcs
dc.relation.urihttps://www.sciencedirect.com/science/article/pii/S0005109820300601cs
dc.rights(C) Elseviercs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/0005-1098/cs
dc.subjectStochastic difference equationsen
dc.subjectProportional feedback controlen
dc.subjectMultiplicative noiseen
dc.subjectAdditive noiseen
dc.subjectRicker mapen
dc.subjectStable cyclesen
dc.titleStabilization of cycles for difference equations with a noisy PF controlen
dc.type.driverarticleen
dc.type.versionsubmittedVersionen
sync.item.dbidVAV-163803en
sync.item.dbtypeVAVen
sync.item.insts2020.11.20 16:54:32en
sync.item.modts2020.11.20 16:14:07en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
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