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dc.description.sponsorshipGefördert im Rahmen des Projekts DEALger
dc.rightsNamensnennung 4.0 International*
dc.subjectDynamical systemeng
dc.subjectRandom numbereng
dc.subjectCircuit theoryeng
dc.subjectDigital circuitseng
dc.titleOn the implementation of large period piece-wise linear Arnold cat mapeng
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.subject.swdTransformation <Mathematik>ger
dcterms.source.issueissue 27
dcterms.source.journalMultimedia Tools and Applicationseng
dcterms.source.volumeVolume 81

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Except where otherwise noted, this item's license is described as Namensnennung 4.0 International