Ouannas Adel, Wang Xiong, Khennaoui Amina-Aicha, Bendoukha Samir, Pham Viet-Thanh, Alsaadi Fawaz E
Department of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa 12002, Algeria.
Institute for Advanced Study, Shenzhen University, Shenzhen 518060, Guangdong, China.
Entropy (Basel). 2018 Sep 20;20(10):720. doi: 10.3390/e20100720.
In this paper, we investigate the dynamics of a fractional order chaotic map corresponding to a recently developed standard map that exhibits a chaotic behavior with no fixed point. This is the first study to explore a fractional chaotic map without a fixed point. In our investigation, we use phase plots and bifurcation diagrams to examine the dynamics of the fractional map and assess the effect of varying the fractional order. We also use the approximate entropy measure to quantify the level of chaos in the fractional map. In addition, we propose a one-dimensional stabilization controller and establish its asymptotic convergence by means of the linearization method.
在本文中，我们研究了与最近开发的一种标准映射相对应的分数阶混沌映射的动力学特性，该标准映射呈现出无不动点的混沌行为。这是首次对无不动点的分数阶混沌映射进行探索的研究。在我们的研究中，我们使用相图和分岔图来研究分数阶映射的动力学特性，并评估改变分数阶的影响。我们还使用近似熵测度来量化分数阶映射中的混沌程度。此外，我们提出了一种一维稳定控制器，并通过线性化方法建立了其渐近收敛性。
