Zur Kurzanzeige

dc.date.accessioned2023-02-03T15:57:07Z
dc.date.available2023-02-03T15:57:07Z
dc.date.issued2022-04-26
dc.identifierdoi:10.17170/kobra-202302037456
dc.identifier.urihttp://hdl.handle.net/123456789/14401
dc.description.sponsorshipGefördert im Rahmen des Projekts DEALger
dc.language.isoeng
dc.rightsNamensnennung 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectDynamical systemeng
dc.subjectRandom numbereng
dc.subjectCircuit theoryeng
dc.subjectDigital circuitseng
dc.subject.ddc510
dc.titleOn the implementation of large period piece-wise linear Arnold cat mapeng
dc.typeAufsatz
dcterms.abstractThis paper presents a piece-wise linear cat map (PWLCM) obtained by perturbing the conventional quantized Arnold cat map (QACM) with a nonlinear term. The effect of the nonlinear term on the dynamics of the QACM is investigated. We show that the eigenvalues, hence the Lyapunov exponents of the PWLCM depend on the initial conditions, which is not the case for the QACM. As a result, the proposed PWLCM is a generalized form of the QACM, whose the period exponentially increases with respect to the precision, thus taking as value 1.09 x 10⁵¹³ for only 10-bit precision; while that of the corresponding QACM is only 768. The nonlinear term increases the sensitivity of the system to the initial conditions, which contributes to increase its period, hence to enhance its complexity. An electronic implementation of both the QACM and the PWLCM in the case of 4-bit precision using Multisim is presented. The proposed architecture of both the QACM and the PWLCM are implemented using Verilog and prototyped on the Zynq 7020 FPGA board. For 4-bit precision, the FPGA implementation performs 1.072 Gbps throughput at 134 MHz maximum frequency. We verified that experimental and simulation behaviors of the proposed system perfectly match, thus confirming the effectiveness of the proposed electronic circuit for exhibiting the expected dynamics in real-time.eng
dcterms.accessRightsopen access
dcterms.creatorHermann, Djeugoue
dcterms.creatorGildas, Gnyamsi Gaetan
dcterms.creatorEyebe Fouda, Jean Sire Armand
dcterms.creatorKoepf, Wolfram
dc.relation.doidoi:10.1007/s11042-022-13175-6
dc.subject.swdSchaltungstheorieger
dc.subject.swdZufallszahlenger
dc.subject.swdSchaltungstheorieger
dc.subject.swdTransformation <Mathematik>ger
dc.type.versionpublishedVersion
dcterms.source.identifiereissn:1573-7721
dcterms.source.issueissue 27
dcterms.source.journalMultimedia Tools and Applicationseng
dcterms.source.pageinfo39003–39020
dcterms.source.volumeVolume 81


Dateien zu dieser Ressource

Thumbnail
Thumbnail

Das Dokument erscheint in:

Zur Kurzanzeige

Namensnennung 4.0 International
Solange nicht anders angezeigt, wird die Lizenz wie folgt beschrieben: Namensnennung 4.0 International