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.
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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