IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v160y2022ics0960077922004258.html
   My bibliography  Save this article

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

Author

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922004258
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112215?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bouallegue, Kais & Chaari, Abdessattar & Toumi, Ahmed, 2011. "Multi-scroll and multi-wing chaotic attractor generated with Julia process fractal," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 79-85.
    2. Wu, Guo-Cheng & Baleanu, Dumitru & Xie, He-Ping & Chen, Fu-Lai, 2016. "Chaos synchronization of fractional chaotic maps based on the stability condition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 374-383.
    3. Karaca, Yeliz & Moonis, Majaz & Baleanu, Dumitru, 2020. "Fractal and multifractional-based predictive optimization model for stroke subtypes’ classification," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    4. Atangana, Abdon & Bouallegue, Ghaith & Bouallegue, Kais, 2020. "New multi-scroll attractors obtained via Julia set mapping," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Rani, Mamta & Agarwal, Rashi, 2009. "Generation of fractals from complex logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 447-452.
    6. Yu, Dakuan & Ta, Wurui & Zhou, Youhe, 2021. "Fractal diffusion patterns of periodic points in the Mandelbrot set," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    7. Yan, Dengwei & Wang, Lidan & Duan, Shukai & Chen, Jiaojiao & Chen, Jiahao, 2021. "Chaotic Attractors Generated by a Memristor-Based Chaotic System and Julia Fractal," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. Xu, Meng & Shang, Pengjian & Zhang, Sheng, 2021. "A novel and effective method to characterize complex systems," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    9. 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.
    10. Wafaa S. Sayed & Ahmed G. Radwan & Hossam A. H. Fahmy, 2015. "Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-23, October.
    11. 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).
    12. Atangana, Abdon & Mekkaoui, Toufik, 2019. "Trinition the complex number with two imaginary parts: Fractal, chaos and fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 366-381.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cheng, Guanghui & Li, Dan & Yao, Yuangen & Gui, Rong, 2023. "Multi-scroll chaotic attractors with multi-wing via oscillatory potential wells," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Dlamini, A. & Doungmo Goufo, E.F., 2023. "Generation of self-similarity in a chaotic system of attractors with many scrolls and their circuit’s implementation," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Liu, Hongwei & He, Ping & Li, Guodong & Xu, Xiangliang & Zhong, Huiyan, 2022. "Multi-directional annular multi-wing chaotic system based on Julia fractals," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    4. 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).
    5. Atangana, Abdon & Bouallegue, Ghaith & Bouallegue, Kais, 2020. "New multi-scroll attractors obtained via Julia set mapping," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    6. Yang, Jie & Li, Chunbiao & Zhang, Qian & Zhang, Xin & Wu, Zhihao & Zhong, Haidong & Liu, Peiqiao & Liu, Zuohua & Tao, Changyuan & Huang, Keyu & Li, Jiaxing & Zheng, Guocan, 2024. "A memristive hyperchaotic oscillator with complete control and its application in the electrolysis of manganese," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    7. Yang, Min & Dong, Chengwei & Pan, Hepeng, 2024. "Generating multi-directional hyperchaotic attractors: A novel multi-scroll system based on Julia fractal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    8. Yan, Dengwei & Wang, Lidan & Duan, Shukai & Chen, Jiaojiao & Chen, Jiahao, 2021. "Chaotic Attractors Generated by a Memristor-Based Chaotic System and Julia Fractal," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. Zhang, Tianxian & Zhao, Yongqi & Xu, Xiangliang & Wu, Si & Gu, Yujuan, 2024. "Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    10. Khalil, Nariman A. & Said, Lobna A. & Radwan, Ahmed G. & Soliman, Ahmed M., 2020. "Emulation circuits of fractional-order memelements with multiple pinched points and their applications," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    11. 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.
    12. Rujira Ouncharoen & Saowaluck Chasreechai & Thanin Sitthiwirattham, 2020. "Existence and Stability Analysis for Fractional Impulsive Caputo Difference-Sum Equations with Periodic Boundary Condition," Mathematics, MDPI, vol. 8(5), pages 1-17, May.
    13. Khennaoui, Amina-Aicha & Ouannas, Adel & Bendoukha, Samir & Grassi, Giuseppe & Lozi, René Pierre & Pham, Viet-Thanh, 2019. "On fractional–order discrete–time systems: Chaos, stabilization and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 150-162.
    14. 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).
    15. Jahanshahi, Hadi & Yousefpour, Amin & Munoz-Pacheco, Jesus M. & Kacar, Sezgin & Pham, Viet-Thanh & Alsaadi, Fawaz E., 2020. "A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    16. Hairong Lin & Chunhua Wang & Fei Yu & Jingru Sun & Sichun Du & Zekun Deng & Quanli Deng, 2023. "A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    17. Cheng, Guanghui & Gui, Rong, 2024. "Understanding Chua system from the perspective of Duffing," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    18. Rawat, Shivam & Prajapati, Darshana J. & Tomar, Anita & Gdawiec, Krzysztof, 2024. "Generation of Mandelbrot and Julia sets for generalized rational maps using SP-iteration process equipped with s-convexity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 148-169.
    19. Du, Feifei & Lu, Jun-Guo, 2021. "New criterion for finite-time synchronization of fractional order memristor-based neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    20. Gu, Yajuan & Wang, Hu & Yu, Yongguang, 2020. "Synchronization for fractional-order discrete-time neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 372(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004258. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.