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On the dynamics, control and synchronization of fractional-order Ikeda map

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  • Ouannas, Adel
  • Khennaoui, Amina-Aicha
  • Odibat, Zaid
  • Pham, Viet-Thanh
  • Grassi, Giuseppe

Abstract

This paper is concerned with a fractional Caputo-difference form of Ikeda map. The dynamics of the proposed map is investigated numerically through phase plots and bifurcation diagrams considered from different perspectives. In addition, a stabilization controller is proposed and the asymptotic convergence of the states is established using the stability theory of linear fractional-order discrete systems. Furthermore, a new synchronization scheme is introduced whereby a new 2D fractional-order chaotic map is considered as the master system and the fractional-order Ikeda map is considered as the response system. Experimental investigations and numerical simulations are also provided to confirm the main findings of the study.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:108-115
    DOI: 10.1016/j.chaos.2019.04.002
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    Cited by:

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    2. 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.
    3. 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).
    4. Pakhare, Sumit S. & Bhalekar, Sachin & Gade, Prashant M., 2022. "Synchronization in coupled integer and fractional-order maps," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    5. Balootaki, Mohammad Ahmadi & Rahmani, Hossein & Moeinkhah, Hossein & Mohammadzadeh, Ardashir, 2020. "On the Synchronization and Stabilization of fractional-order chaotic systems: Recent advances and future perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    6. Motaeb Eid Alshammari & Makbul A. M. Ramli & Ibrahim M. Mehedi, 2021. "A New Chaotic Artificial Bee Colony for the Risk-Constrained Economic Emission Dispatch Problem Incorporating Wind Power," Energies, MDPI, vol. 14(13), pages 1-24, July.
    7. Ávalos-Ruiz, L.F. & Gómez-Aguilar, J.F. & Atangana, A. & Owolabi, Kolade M., 2019. "On the dynamics of fractional maps with power-law, exponential decay and Mittag–Leffler memory," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 364-388.
    8. Liu, Xianggang & Ma, Li, 2020. "Chaotic vibration, bifurcation, stabilization and synchronization control for fractional discrete-time systems," Applied Mathematics and Computation, Elsevier, vol. 385(C).

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