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On Chaos and Complexity Analysis for a New Sine-Based Memristor Map with Commensurate and Incommensurate Fractional Orders

Author

Listed:
  • Tareq Hamadneh

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

  • Abderrahmane Abbes

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

  • Hassan Al-Tarawneh

    (Department of Data Sciences and Artificial Intelligence, Al-Ahliyya Amman University, Amman 11931, Jordan)

  • Gharib Mousa Gharib

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

  • Wael Mahmoud Mohammad Salameh

    (Faculty of Information Technology, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates)

  • Maha S. Al Soudi

    (Department of Basic Scientific Sciences, Applied Science Private University, Amman 11931, Jordan)

  • Adel Ouannas

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

Abstract

In this study, we expand a 2D sine map via adding the discrete memristor to introduce a new 3D fractional-order sine-based memristor map. Under commensurate and incommensurate orders, we conduct an extensive exploration and analysis of its nonlinear dynamic behaviors, employing diverse numerical techniques, such as analyzing Lyapunov exponents, visualizing phase portraits, and plotting bifurcation diagrams. The results emphasize the sine-based memristor map’s sensitivity to fractional-order parameters, resulting in the emergence of distinct and diverse dynamic patterns. In addition, we employ the sample entropy ( S a m p E n ) method and C 0 complexity to quantitatively measure complexity, and we also utilize the 0–1 test to validate the presence of chaos in the proposed fractional-order sine-based memristor map. Finally, MATLAB simulations are be executed to confirm the results provided.

Suggested Citation

  • Tareq Hamadneh & Abderrahmane Abbes & Hassan Al-Tarawneh & Gharib Mousa Gharib & Wael Mahmoud Mohammad Salameh & Maha S. Al Soudi & Adel Ouannas, 2023. "On Chaos and Complexity Analysis for a New Sine-Based Memristor Map with Commensurate and Incommensurate Fractional Orders," Mathematics, MDPI, vol. 11(20), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4308-:d:1260814
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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. Dmitri B. Strukov & Gregory S. Snider & Duncan R. Stewart & R. Stanley Williams, 2008. "The missing memristor found," Nature, Nature, vol. 453(7191), pages 80-83, May.
    3. Lin, Hairong & Wang, Chunhua & Du, Sichun & Yao, Wei & Sun, Yichuang, 2023. "A family of memristive multibutterfly chaotic systems with multidirectional initial-based offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
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