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The fractional difference form of sine chaotification model

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  • Li, Yuqing
  • He, Xing
  • Zhang, Wei

Abstract

To improve the chaos complexity of existing chaotic maps, the fractional difference form of sine chaotification model (FSCM) is proposed in this paper based on discrete fractional calculus. In order to show its effect, we apply it to three chaotic maps. And the bifurcation diagrams and Lyapunov exponent of the generated new map are studied numerically. The experimental results show that FSCM has more stable and efficient performance. In addition, the dynamic behavior of the generated new map varies with the fractional order, which can be observed through analysis. Finally, FSCM is used for image encryption to show its performance in practical applications. The analysis of the results shows that the chaotic behavior of the fractional map generated by FSCM is more complex and its encryption effect is better.

Suggested Citation

  • Li, Yuqing & He, Xing & Zhang, Wei, 2020. "The fractional difference form of sine chaotification model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920301764
    DOI: 10.1016/j.chaos.2020.109774
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    References listed on IDEAS

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    1. Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 285-294.
    2. Khennaoui, Amina-Aicha & Ouannas, Adel & Bendoukha, Samir & Grassi, Giuseppe & Lozi, René Pierre & Pham, Viet-Thanh, 2019. "On fractional–order discrete–time systems: Chaos, stabilization and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 150-162.
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    Cited by:

    1. Al-Raeei, Marwan, 2021. "Applying fractional quantum mechanics to systems with electrical screening effects," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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