The unified criteria are analyzed on the global dissipativity and stability for the delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) in this article. First, based on the comprehensive knowledge about multidimensional algebra, fractional derivatives, and nonsmooth analysis, we establish the unified model for the studied FSMVMNNs in order to propose a more uniform method to analyze the dynamic behaviors of multidimensional neural networks. Then, by mainly applying the Lyapunov method, employing several new lemmas, and solving some mathematical difficulties, without any separation, we acquire the unified and concise criteria. The derived criteria have many advantages in a smaller calculation, lower conservatism, more diversity, and higher flexibility. Finally, we provide two numerical examples to express the availability and improvements of the theoretical results.

中文翻译：

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时滞分数阶多维忆阻神经网络全局耗散性和稳定性的统一分析


本文采用统一准则对多维忆阻神经网络（FSMVMNN）延迟分数阶系统的全局耗散性和稳定性进行了分析。首先，基于多维代数、分数阶导数和非光滑分析的综合知识，我们为所研究的 FSMVMNN 建立了统一的模型，以便提出一种更统一的方法来分析多维神经网络的动态行为。然后，主要应用李亚普诺夫方法，采用几个新的引理，解决一些数学难题，没有任何分离，我们得到了统一而简洁的判据。导出的准则具有计算量小、保守性低、多样性强、灵活性高等优点。最后，我们提供了两个数值例子来表达理论结果的可用性和改进。