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The New Four-Dimensional Fractional Chaotic Map with Constant and Variable-Order: Chaos, Control and Synchronization

Author

Listed:
  • Tareq Hamadneh

    (Department of Mathematics, Faculty of Science, Al Zaytoonah University of Jordan, Amman 11931, Jordan)

  • Souad Bensid Ahmed

    (Department of Mathematics, The University of Jordan, Amman 11942, Jordan)

  • Hassan Al-Tarawneh

    (Department of Data Sciences and Artificial Intelligence, Al-Ahliyya Amman University, Amman 11942, Jordan)

  • Omar Alsayyed

    (Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan)

  • Gharib Mousa Gharib

    (Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan)

  • Maha S. Al Soudi

    (Department of Basic Scientific Sciences, Applied Science Private University, Amman 11942, Jordan)

  • Abderrahmane Abbes

    (Laboratory of Mathematics, Dynamics and Modelization, Badji Mokhtar-Annaba University, Annaba 23000, Algeria)

  • Adel Ouannas

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

Abstract

Using fractional difference equations to describe fractional and variable-order maps, this manuscript discusses the dynamics of the discrete 4D sinusoidal feedback sine iterative chaotic map with infinite collapse (ICMIC) modulation map (SF-SIMM) with fractional-order. Also, it presents a novel variable-order version of SF-SIMM and discusses their chaotic dynamic behavior by employing a distinct function for the variable fractional-order. To establish the existence of chaos in the suggested discrete SF-SIMM, some numerical methods such as phase plots, bifurcation and largest Lyapunov exponent diagrams, C 0 complexity and 0–1 test are utilized. After that, two different control schemes are used for the conceived discrete system. The states are stabilized and asymptotically forced towards zero by the first controller. The second controller is used to synchronize a pair of maps with non–identical parameters. Finally, MATLAB simulations will be executed to confirm the results provided.

Suggested Citation

  • Tareq Hamadneh & Souad Bensid Ahmed & Hassan Al-Tarawneh & Omar Alsayyed & Gharib Mousa Gharib & Maha S. Al Soudi & Abderrahmane Abbes & Adel Ouannas, 2023. "The New Four-Dimensional Fractional Chaotic Map with Constant and Variable-Order: Chaos, Control and Synchronization," Mathematics, MDPI, vol. 11(20), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4332-:d:1262232
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    References listed on IDEAS

    as
    1. Peng, Yuexi & Liu, Jun & He, Shaobo & Sun, Kehui, 2023. "Discrete fracmemristor-based chaotic map by Grunwald–Letnikov difference and its circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    2. Jiang Wang & Yang Gu & Kang Rong & Quan Xu & Xi Zhang, 2022. "Memristor-Based Lozi Map with Hidden Hyperchaos," Mathematics, MDPI, vol. 10(19), pages 1-12, 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).
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