具有时滞效应的BAM神经网络的稳定性与分岔
Stability and Bifurcation of BAM Neural Network with Time Delay Effect
DOI: 10.12677/AAM.2023.126273, PDF,   
作者: 和光珠：云南省下关第一中学，云南 大理
关键词: BAM；神经网络；稳定性；Hopf分岔；时滞；BAM； Neural Network； Stability； Hopf Bifurcation； Time Delay
摘要: 本文研究了一个具有时滞效应的BAM神经网络模型。研究表明当时滞超过一定的临界值时，系统出现Hopf分岔。本文利用规范型理论和中心流形定理得到Hopf分岔的方向和周期解稳定性的条件，并进行了数值模拟，得到了时滞可以诱导BAM神经网络从稳定态转为振荡态的结果，为神经网络的非线性动态特性研究提供了理论依据。
Abstract: This paper studies a BAM neural network model with time delay effect. Studies show that when the hysteresis exceeds a certain critical value, Hopf bifurcation occurs in the system. In this paper, the direction of Hopf bifurcation and the stability of periodic solution are obtained by using the canoni-cal theory and the central manifold theorem, and the numerical simulation is carried out to obtain the result that time delay can induce the transformation of BAM neural network from a stable state to an oscillating state, which provides a theoretical basis for the study of the nonlinear dynamic characteristics of neural network.
文章引用：和光珠. 具有时滞效应的BAM神经网络的稳定性与分岔[J]. 应用数学进展, 2023, 12(6): 2718-2735. https://doi.org/10.12677/AAM.2023.126273

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