Abstract The stability and synchronization problems are addressed in this study for the memristor-based fractional-order fuzzy cellular neural networks with multiple delays. By using the Laplace transform method, fractional-order calculus approach and the method of complex function, three exponential stability criteria are derived. Compared with the existing results of the above system, the novel exponentially stable and synchronization conditions are first proposed. The obtained results can be applied not only to fractional-order systems, but also to integer-order systems. A two-dimension example and a three-dimension example and a practical example are given to illustrate the validity and merits.

中文翻译：

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具有多重延迟的基于忆阻器的分数阶模糊细胞神经网络的指数稳定性和同步性

摘要 本研究针对具有多重延迟的基于忆阻器的分数阶模糊细胞神经网络解决了稳定性和同步问题。利用拉普拉斯变换法、分数阶微积分法和复函数法，推导出三个指数稳定性判据。与上述系统的现有结果相比，首次提出了新颖的指数稳定和同步条件。所得结果不仅适用于分数阶系统，也适用于整数阶系统。给出一个二维例子和一个三维例子以及一个实际例子来说明有效性和优点。