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The Dynamics and Control of the Fractional Forms of Some Rational Chaotic Maps
Journal of Systems Science and Complexity ( IF 2.1 ) Pub Date : 2020-04-28 , DOI: 10.1007/s11424-020-8326-6
Adel Ouannas , Amina-Aicha Khennaoui , Samir Bendoukha , Zhen Wang , Viet-Thanh Pham

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.

中文翻译:

一些有理混沌图的分数形式的动力学和控制

本文提出了基于Rulkov,Chang和Zeraoulia-Sprott有理图的三个分数阶离散混沌系统。借助相图和分叉图研究了拟议地图的动力学。针对这三个图分别提出了一种自适应稳定方案,并利用李雅普诺夫方法建立了状态的收敛性。此外,提出了一种组合同步方案,其中分数Rulkov和Chang图的组合被同步到分数Zeraoulia-Sprott图。数值结果用于证实本文的发现。
更新日期:2020-04-28
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