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The Dynamics and Control of the Fractional Forms of Some Rational Chaotic Maps

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Abstract

This paper proposes three fractional discrete chaotic systems based on the Rulkov, Chang, and Zeraoulia-Sprott rational maps. The dynamics of the proposed maps are investigated by means of phase plots and bifurcations diagrams. Adaptive stabilization schemes are proposed for each of the three maps and the convergence of the states is established by using the Lyapunov method. Furthermore, a combination synchronization scheme is proposed whereby a combination of the fractional Rulkov and Chang maps is synchronized to the fractional Zeraoulia-Sprott map. Numerical results are used to confirm the findings of the paper.

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Acknowledgements

The authors acknowledge Prof. Guanrong Chen, Department of Electronic Engineering, City University of Hong Kong for suggesting many helpful references. The author Adel Ouannas was supported by the Directorate General for Scientific Research and Technological Development of Algeria.

Author information

Authors and Affiliations

  1. Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, Tebessa, 12002, Algeria

    Adel Ouannas

  2. Department of Mathematics and Computer Sciences, University of Larbi Ben M’hidi, Oum El Bouaghi, Algeria

    Amina-Aicha Khennaoui

  3. Department of Electrical Engineering, College of Engineering, Yanbu, Taibah University, Medina, Saudi Arabia

    Samir Bendoukha

  4. Shaanxi Engineering Research Center of Controllable Neutron Source, School of Science, Xijing University, Xi’an, 710123, China

    Zhen Wang

  5. Faculty of Electrical and Electronic Engineering, Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong district, Hanoi, 100000, Vietnam

    Viet-Thanh Pham

  6. A&A Green Phoenix Group, Phenikaa Research and Technology Institute (PRATI), 167 Hoang Ngan, Hanoi, 100000, Vietnam

    Viet-Thanh Pham

Authors
  1. Adel Ouannas
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  2. Amina-Aicha Khennaoui
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  3. Samir Bendoukha
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  4. Zhen Wang
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  5. Viet-Thanh Pham
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Corresponding authors

Correspondence to Adel Ouannas, Amina-Aicha Khennaoui, Samir Bendoukha, Zhen Wang or Viet-Thanh Pham.

Additional information

This paper was supported by the Natural Science Foundation of China under Grant Nos. 11726624, 11726623, 61473237, the Natural Science Basic Research Plan in Shaanxi Province of China under Grant No. 2018GY-091, the Natural Science Basic Research Plan in Shandong Province of China under Grant No. ZR2017PA008.

This paper was recommended for publication by Editor CHEN Jie.

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Ouannas, A., Khennaoui, AA., Bendoukha, S. et al. The Dynamics and Control of the Fractional Forms of Some Rational Chaotic Maps. J Syst Sci Complex 33, 584–603 (2020). https://doi.org/10.1007/s11424-020-8326-6

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  • DOI: https://doi.org/10.1007/s11424-020-8326-6

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