Multistablity analysis and formation of spiral wave in the fractional-order nonlinear systems is a recent hot topic. In this paper, dynamics, coexisting attractors, complexity, and synchronization of the fractional-order memristor-based hyperchaotic Lü system are investigated numerically by means of bifurcation diagram, Lyapunov exponents (LEs), chaos diagram, and sample entropy (SampEn) algorithm. The results show that the system has rich dynamics and high complexity. Meanwhile, coexisting attractors in the system are observed and hidden dynamics are illustrated by changing the initial conditions. Finally, the network based on the system is built, and the emergence of spiral waves is investigated and chimera states are observed.

中文翻译：

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基于分数阶忆阻器的超混沌Lü系统中没有平衡点的多重稳定性和螺旋波的形成

分数阶非线性系统的多稳性分析和螺旋波的形成是近期的热门话题。本文通过分叉图，李雅普诺夫指数（LEs），混沌图和样本熵（SampEn）算法，对基于分数阶忆阻器的超混沌Lü系统的动力学，共存吸引子，复杂性和同步进行了数值研究。结果表明，该系统具有丰富的动力学特性和较高的复杂度。同时，观察系统中共存的吸引子，并通过更改初始条件来说明隐藏的动力学。最后，建立了基于系统的网络，研究了螺旋波的出现并观察了嵌合体状态。