比例时滞复值BAM神经网络的稳定性研究
Research on Stability of Proportionally Delayed Complex-Valued BAM Neural Networks
DOI: 10.12677/aam.2025.145273, PDF,   
作者: 罗 敏, 熊 梅*：云南财经大学统计与数学学院，云南 昆明；陈龙伟, 余益民：云南财经大学云南省服务计算重点实验室，云南 昆明；云南财经大学智能应用研究院，云南 昆明
关键词: 复值BAM神经网络；比例时滞；稳定性；Banach不动点定理；Complex-Valued BAM Neural Networks； Proportional Delay； Stability； Banach Fixed Point Theorem
摘要: BAM (Bidirectional Associative Memory)神经网络以其双向异联想性、较强的学习和自适应能力以及噪声容忍性好等特点，在模式分类和识别等方面具有广泛的应用前景。与实值神经网络相比，复值神经网络是一种基于复数运算的神经网络模型，可以有效地刻画如图像、声音等具有多个维度的信号，减少对信号的近似，从而提高模型的精度。因此，本文主要研究了一类比例时滞复值BAM神经网络的全局指数稳定性，利用Banach不动点定理，给出了这类神经网络全局指数稳定的充分条件。最后，举出具体的数值算例验证了结果的有效性。
Abstract: BAM (Bidirectional Associative Memory) neural networks have significant potential for applications in pattern classification and recognition due to their bidirectional associations, robust learning and adaptive capabilities, and excellent noise tolerance. Compared with real-valued neural networks, complex-valued neural networks, which are based on complex operations, can more effectively represent multi-dimensional signals such as images and sounds. They reduce signal approximation errors and enhance model accuracy. Consequently, this paper primarily focuses on the global exponential stability of a class of proportional delay complex-valued BAM neural networks. By applying the Banach fixed point theorem, the sufficient conditions for the global exponential stability of these neural networks are given. Finally, a numerical example is provided to demonstrate the effectiveness of the results.
文章引用：罗敏, 熊梅, 陈龙伟, 余益民. 比例时滞复值BAM神经网络的稳定性研究[J]. 应用数学进展, 2025, 14(5): 434-449. https://doi.org/10.12677/aam.2025.145273

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