具有脉冲的混合时滞Hopfield神经网络的全局渐近稳定性
Global Asymptotic Stability of Hopfield Neural Networks with Mixed Delays and Impulses
DOI: 10.12677/AAM.2021.1011417, PDF,    国家自然科学基金支持
作者: 张雪莹*, 陈展衡#：伊犁师范大学数学与统计学院，新疆 伊宁
关键词: 脉冲；混合时滞；Hopfield神经网络；全局渐近稳定性；Impulse； Mixed Time Delay； Hopfield Neural Network； Global Asymptotic Stability
摘要: 本文研究一类具有脉冲的混合时滞Hopfield神经网络的全局渐近稳定性，首先利用Brouwer不动点定理和矩阵谱半径证明系统平衡点的存在性和唯一性，再利用Barbalat引理以及构造合适的Lyapunov函数，讨论系统的全局渐近稳定性，最后利用数值仿真验证结论的有效性。
Abstract: This paper studies the global asymptotic stability of a class of Hopfield neural networks with impulsive mixed delays. Firstly, the Brouwer fixed point theorem and the matrix spectral radius are used to prove the existence and uniqueness of the equilibrium point of the system, and then use Barbalat’s lemma and construct a suitable Lyapunov function to discuss the global asymptotic stability of the system. Finally use numerical simulation to verify the validity of the conclusions.
文章引用：张雪莹, 陈展衡. 具有脉冲的混合时滞Hopfield神经网络的全局渐近稳定性[J]. 应用数学进展, 2021, 10(11): 3923-3931. https://doi.org/10.12677/AAM.2021.1011417

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