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Special Fractional-Order Map and Its Realization

Author

Listed:
  • Amina-Aicha Khennaoui

    (Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria)

  • Adel Ouannas

    (Department of Mathematics and Computer Sciences, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria)

  • Shaher Momani

    (Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman 20550, United Arab Emirates
    Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan)

  • Othman Abdullah Almatroud

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Mohammed Mossa Al-Sawalha

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Salah Mahmoud Boulaaras

    (Department of Mathematics, College of Sciences and Arts in ArRass, Qassim University, Buraydah 51452, Saudi Arabia)

  • Viet-Thanh Pham

    (Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam)

Abstract

Recent works have focused the analysis of chaotic phenomena in fractional discrete memristor. However, most of the papers have been related to simulated results on the system dynamics rather than on their hardware implementations. This work reports the implementation of a new chaotic fractional memristor map with “hidden attractors”. The fractional memristor map is developed based on a memristive map by using the Grunwald–Letnikov difference operator. The fractional memristor map has flexible fixed points depending on a system’s parameters. We study system dynamics for different values of the fractional orders by using bifurcation diagrams, phase portraits, Lyapunov exponents, and the 0–1 test. We see that the fractional map generates rich dynamical behavior, including coexisting hidden dynamics and initial offset boosting.

Suggested Citation

  • Amina-Aicha Khennaoui & Adel Ouannas & Shaher Momani & Othman Abdullah Almatroud & Mohammed Mossa Al-Sawalha & Salah Mahmoud Boulaaras & Viet-Thanh Pham, 2022. "Special Fractional-Order Map and Its Realization," Mathematics, MDPI, vol. 10(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4474-:d:985478
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    References listed on IDEAS

    as
    1. Peng, Yuexi & Sun, Kehui & Peng, Dong & Ai, Wei, 2019. "Dynamics of a higher dimensional fractional-order chaotic map," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 96-107.
    2. Sid Ahmed Ould Beinane & Mohamed Reda Lemnaouar & Rabie Zine & Younes Louartassi & Akif Akgul, 2022. "Stability Analysis of COVID-19 Epidemic Model of Type SEIQHR with Fractional Order," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-14, September.
    3. Wang, Lingyu & Sun, Kehui & Peng, Yuexi & He, Shaobo, 2020. "Chaos and complexity in a fractional-order higher-dimensional multicavity chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Ahlem Gasri & Amina-Aicha Khennaoui & Adel Ouannas & Giuseppe Grassi & Apostolos Iatropoulos & Lazaros Moysis & Christos Volos & M. De Aguiar, 2022. "A New Fractional-Order Map with Infinite Number of Equilibria and Its Encryption Application," Complexity, Hindawi, vol. 2022, pages 1-18, February.
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    Cited by:

    1. Othman Abdullah Almatroud & Viet-Thanh Pham, 2023. "Building Fixed Point-Free Maps with Memristor," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    2. Martínez-Fuentes, Oscar & Díaz-Muñoz, Jonathan Daniel & Muñoz-Vázquez, Aldo Jonathan & Tlelo-Cuautle, Esteban & Fernández-Anaya, Guillermo & Cruz-Vega, Israel, 2024. "Family of controllers for predefined-time synchronization of Lorenz-type systems and the Raspberry Pi-based implementation," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    3. Fei Yu & Wuxiong Zhang & Xiaoli Xiao & Wei Yao & Shuo Cai & Jin Zhang & Chunhua Wang & Yi Li, 2023. "Dynamic Analysis and FPGA Implementation of a New, Simple 5D Memristive Hyperchaotic Sprott-C System," Mathematics, MDPI, vol. 11(3), pages 1-15, January.

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