In this paper, a type of delayed Clifford-valued memristor-based neural networks (CLVMNNs) with impulsive disturbances is established, and the global exponential stability is investigated by using generalized norm. Firstly, the n-dimensional Clifford-valued systems are decomposed into -dimensional real-valued systems to address the non-commutativity problem of the multiplication of Clifford numbers. Secondly, the generalized ∞-norm and 1-norm are introduced to induce the global exponential stability for CLVMNNs, and two special Lyapunov functionals are established to prove the stability. Thirdly, the strict assumption of the boundedness of activation function in previous research is loosened, and some less conservative conditions of stability are obtained based on the constructed Lyapunov functionals. Finally, the theoretical results are verified by two numerical simulations, and an image encryption scheme is proposed to show the application in real world situation based on the delayed CLVMNNs.

中文翻译：

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具有脉冲扰动的Clifford值忆阻器神经网络的稳定性分析及其在图像加密中的应用

本文建立了一种带有脉冲扰动的延迟克利福德值忆阻器神经网络（CLVMNN），并利用广义范数研究了全局指数稳定性。首先，将n维Clifford值系统分解为维实值系统，解决Clifford数乘法的非交换性问题。其次，引入广义的 ∞-范数和 1-范数来引入 CLVMNN 的全局指数稳定性，并建立两个特殊的 Lyapunov 泛函来证明稳定性。再次，放松了以往研究中对激活函数有界性的严格假设，基于构造的Lyapunov泛函得到了一些不太保守的稳定性条件。最后，通过两次数值模拟验证了理论结果，并提出了一种基于延迟 CLVMNN 的图像加密方案，以展示其在实际情况中的应用。