Abstract This paper addresses the problems of stabilization and synchronization control of the fractional-order quaternion-valued fuzzy memristive neural networks. By means of the contraction mapping theorem, the corresponding conditions are established for the existence and uniqueness of the equilibrium point (EP), subsequently, the corresponding stability analysis are proposed by two suitable controllers. What should be mentioned is that, a vector ordering approach is developed to determine the “magnitude” of two different quaternions, as a result, the closed convex hull proposed by quaternion connections can be easily derived. Finally, two simulation examples are utilized to illustrate the effectiveness of the proposed control method.

中文翻译：

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分数阶四元数值模糊忆阻神经网络的动态分析：向量排序方法

摘要 本文解决了分数阶四元数值模糊忆阻神经网络的稳定性和同步控制问题。借助收缩映射定理，建立了平衡点（EP）的存在唯一性的相应条件，随后通过两个合适的控制器提出了相应的稳定性分析。应该提到的是，开发了一种向量排序方法来确定两个不同四元数的“大小”，因此可以很容易地推导出由四元数连接提出的封闭凸包。最后，利用两个仿真实例来说明所提出的控制方法的有效性。