On the implementation of large period piece-wise linear Arnold cat map
Classification / Keywords
Sponsor
Citation
In: Multimedia Tools and Applications Volume 81 / issue 27 (2022-04-26) , S. 39003–39020; eissn:1573-7721
Collections
This 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.
@article{doi:10.17170/kobra-202302037456, author ={Hermann, Djeugoue and Gildas, Gnyamsi Gaetan and Eyebe Fouda, Jean Sire Armand and Koepf, Wolfram}, title ={On the implementation of large period piece-wise linear Arnold cat map}, keywords ={510 and Schaltungstheorie and Zufallszahlen and Schaltungstheorie and Transformation }, copyright ={http://creativecommons.org/licenses/by/4.0/}, language ={en}, journal ={Multimedia Tools and Applications}, year ={2022-04-26} }