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Fractional X-shape controllable multi-scroll attractor with parameter effect and FPGA automatic design tool software

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  • Soliman, Nancy S.
  • Tolba, Mohammed F.
  • Said, Lobna A.
  • Madian, Ahmed H.
  • Radwan, Ahmed G.

Abstract

This paper proposes a new fractional-order multi-scrolls chaotic system. More complex systems and flexible ranges of the chaotic behavior are obtained due to the extra parameters added by the fractional-order. The proposed system has novel complex chaotic behaviors. The effect of changing the system parameters on the system behavior is investigated and their bifurcation diagrams have been provided. The MLE for the proposed system in integer and fractional domain has been discussed. It shows that the proposed chaotic system is richer in the case of fractional-order. A novel FPGA design automation tool for the proposed system is also proposed. It provides an optimized FPGA implementation of the system according to different system parameters. Additionally, it provides a facility and fast way to accelerate the design process for the developer to design their own module while applying the system in different applications. The proposed tool has been tested using Xilinx's Virtex-5 XC5VLX50T FPGA and verified using MATLAB. The experimental results are provided for different design peripherals options. Finally, a procedure to generalize the proposed tool to involve any other chaotic system is presented.

Suggested Citation

  • Soliman, Nancy S. & Tolba, Mohammed F. & Said, Lobna A. & Madian, Ahmed H. & Radwan, Ahmed G., 2019. "Fractional X-shape controllable multi-scroll attractor with parameter effect and FPGA automatic design tool software," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 292-307.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:292-307
    DOI: 10.1016/j.chaos.2019.05.028
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    Cited by:

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    3. AboAlNaga, BahaaAlDeen M. & Said, Lobna A. & Madian, Ahmed H. & Radwan, Ahmed G., 2021. "Analysis and FPGA of semi-fractal shapes based on complex Gaussian map," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Jia, Hongyan & Liu, Jingwen & Li, Wei & Du, Meng, 2023. "A family of new generalized multi-scroll Hamiltonian conservative chaotic flows on invariant hypersurfaces and FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    5. Kuate, Paul Didier Kamdem & Tchendjeu, Achille Ecladore Tchahou & Fotsin, Hilaire, 2020. "A modified Rössler prototype-4 system based on Chua’s diode nonlinearity : Dynamics, multistability, multiscroll generation and FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    6. 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).

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