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Chaos and complexity in a fractional-order higher-dimensional multicavity chaotic map

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  • Wang, Lingyu
  • Sun, Kehui
  • Peng, Yuexi
  • He, Shaobo

Abstract

In this paper, a fractional-order higher-dimensional multicavity chaotic map is investigated in the Caputo discrete delta’s sense. The numerical formula of discrete fractional-order chaotic map is deduced by utilizing the discrete fractional calculus (DFC). Taking a two-demensional model as an example, the dynamical analysis of the fractional-order multicavity chaotic map is carried out in detail by means of attractors, bifurcation diagrams, permutation entropy complexity and distribution characteristics. Moreover, there is a comparison between the fractional-order system and its integer-order counterpart for their behaviors. It shows that the fractional-order system has richer dynamical behaviors, higher complexity and more uniform distribution characteristics, which means that the fractional-order system has better engineering application.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304345
    DOI: 10.1016/j.chaos.2019.109488
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    References listed on IDEAS

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    Cited by:

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    2. 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.
    3. Zhang, Sen & Zheng, Jiahao & Wang, Xiaoping & Zeng, Zhigang, 2021. "A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    4. Zambrano-Serrano, Ernesto & Bekiros, Stelios & Platas-Garza, Miguel A. & Posadas-Castillo, Cornelio & Agarwal, Praveen & Jahanshahi, Hadi & Aly, Ayman A., 2021. "On chaos and projective synchronization of a fractional difference map with no equilibria using a fuzzy-based state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    5. 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.

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