具比例时滞的Cohen-Grossberg神经网络的稳定性研究
Stability Analysis of Cohen-Grossberg Neural Networks with Proportional Delays
摘要: 本文研究了具有比例时滞的Cohen-Grossberg神经网络的全局指数稳定性。首先通过适当的变换，将比例时滞的Cohen-Grossberg神经网络模型等价的转换为具有常时滞的Cohen-Grossberg神经网络模型。通过应用M-矩阵理论和不等式技巧建立了全局指数稳定性的充分条件。通过数值仿真来验证了所得结论的有效性。
Abstract: This paper investigates global exponential stability of Cohen-Grossberg neural networks with proportional delays. Firstly, the Cohen-Grossberg neural networks model with proportional delay is equivalent to the Cohen-Grossberg neural networks model with constant delay through appropriate transformation. Sufficient conditions for global exponential stability are established by applying M-matrix theory and inequality techniques. The validity of the obtained conclusions is verified by numerical simulation.
文章引用：古力加依娜•木合亚提, 姑丽加玛丽•麦麦提艾力. 具比例时滞的Cohen-Grossberg神经网络的稳定性研究[J]. 理论数学, 2023, 13(4): 996-1006. https://doi.org/10.12677/PM.2023.134105

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