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FPGA realization of fractals based on a new generalized complex logistic map

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Listed:
  • Mohamed, Sara M.
  • Sayed, Wafaa S.
  • Said, Lobna A.
  • Radwan, Ahmed G.

Abstract

This paper introduces a new generalized complex logistic map and the FPGA realization of a corresponding fractal generation application. The chaotic properties of the proposed map are studied through the stability conditions, bifurcation behavior and maximum Lyapunov exponent (MLE). A relation between the mathematical analysis and fractal behavior is demonstrated, which enables formulating the fractal limits. A compact fractal generation process is presented, which results in designing and implementing an optimized hardware architecture. An efficient FPGA implementation of the fractal behavior is validated experimentally on Artix-7 FPGA board. Two examples of fractal implementation are verified, yielding frequencies of 34.593MHz and 31.979MHz and throughputs of 0.415 Gbit/s, 0.384 Gbit/s. Compared to recent related works, the proposed implementation demonstrates its efficient hardware utilization and suitability for potential applications.

Suggested Citation

  • Mohamed, Sara M. & Sayed, Wafaa S. & Said, Lobna A. & Radwan, Ahmed G., 2022. "FPGA realization of fractals based on a new generalized complex logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004258
    DOI: 10.1016/j.chaos.2022.112215
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    References listed on IDEAS

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