Abstract This paper studies the dynamics of two fractional-order chaotic maps based on two standard chaotic maps with sine terms. The dynamic behavior of this map is analyzed using numerical tools such as phase plots, bifurcation diagrams, Lyapunov exponents and 0–1 test. With the change of fractional-order, it is shown that the proposed fractional maps exhibit a range of different dynamical behaviors including coexisting attractors. The existence of coexistence attractors is depicted by plotting bifurcation diagram for two symmetrical initial conditions. In addition, three control schemes are introduced. The first two controllers stabilize the states of the proposed maps and ensure their convergence to zero asymptotically whereas the last synchronizes a pair of non-identical fractional maps. Numerical results are used to verify the findings.

中文翻译：

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带正弦项的分数阶混沌映射的动力学与控制

摘要 本文基于两个带正弦项的标准混沌图研究了两个分数阶混沌图的动力学。该地图的动态行为使用数值工具进行分析，例如相位图、分叉图、Lyapunov 指数和 0-1 检验。随着分数阶的变化，表明所提出的分数映射表现出一系列不同的动力学行为，包括共存的吸引子。通过绘制两个对称初始条件的分岔图来描述共存吸引子的存在。此外，还介绍了三种控制方案。前两个控制器稳定所提出的映射的状态并确保它们渐近地收敛到零，而最后一个控制器同步一对不相同的分数映射。数值结果用于验证结果。