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The Discrete Fractional Variable-Order Tinkerbell Map: Chaos, 0–1 Test, and Entropy

Author

Listed:
  • Souad Bensid Ahmed

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

  • Adel Ouannas

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

  • Mohammed Al Horani

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

  • Giuseppe Grassi

    (Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy)

Abstract

The dynamics of the Caputo-fractional variable-order difference form of the Tinkerbell map are studied. The phase portraits, bifurcation, and largest Lyapunov exponent (LLE) were employed to demonstrate the presence of chaos over a different fractional variable-order and establish the nature of the dynamics. In addition, the 0–1 test tool was used to detect chaos. Finally, the numerical results were confirmed using the approximate entropy.

Suggested Citation

  • Souad Bensid Ahmed & Adel Ouannas & Mohammed Al Horani & Giuseppe Grassi, 2022. "The Discrete Fractional Variable-Order Tinkerbell Map: Chaos, 0–1 Test, and Entropy," Mathematics, MDPI, vol. 10(17), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3173-:d:905733
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    References listed on IDEAS

    as
    1. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    2. Shichang Ma & Yufeng Xu & Wei Yue, 2012. "Numerical Solutions of a Variable-Order Fractional Financial System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, September.
    3. Wang, Limin & Song, Qiankun, 2020. "Pricing policies for dual-channel supply chain with green investment and sales effort under uncertain demand," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 79-93.
    4. Ouannas, Adel & Khennaoui, Amina-Aicha & Odibat, Zaid & Pham, Viet-Thanh & Grassi, Giuseppe, 2019. "On the dynamics, control and synchronization of fractional-order Ikeda map," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 108-115.
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