FPGA implementation of two fractional order chaotic systems

Mohammed F. Tolba, Amr M. AbdelAty, Nancy S. Soliman, Lobna A. Said, Ahmed H. Madian, Ahmad Taher Azar, Ahmed G. Radwan

    Research output: Contribution to journalArticlepeer-review

    164 Scopus citations


    This paper discusses the FPGA implementation of the fractional-order derivative as well as two fractional-order chaotic systems where one of them has controllable multi-scroll attractors. The complete hardware architecture of the Grünwald-Letnikov (GL) differ-integral is realized with different memory window sizes. As an application of the proposed circuit, a complete fractional-order FPGA implementation of Liu chaotic system is introduced with different fractional-orders. Moreover, a fractional-order controllable heart and V-shape multi-scrolls chaotic systems are verified in the case of symmetric and asymmetric cases. Different interesting attractors are realized under various parametric changes with distinct step sizes for different fractional-orders. To verify the chaotic behavior of many generating attractors, the Maximum Lyapunov Exponent (MLE) is calculated for such systems. The designs have been simulated using Xilinx ISE 14.5 and realized on Xilinx FPGA Virtex 5 XC5VLX50T. The achieved throughputs are: 4.4 Gbit/s for GL, 1.986 Gbit/s for Liu system, and 2.921 Gbit/s for V-Shape multi-scroll attractor.

    Original languageBritish English
    Pages (from-to)162-172
    Number of pages11
    JournalAEU - International Journal of Electronics and Communications
    StatePublished - Aug 2017


    • Chaotic systems
    • FPGA
    • Fractional order
    • Liu system
    • Multi-scroll
    • V-Shape


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