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

作　　者：和光珠 

机构地区：[1]云南省下关第一中学,云南 大理

出　　处：《应用数学进展》2023年第6期2718-2735,共18页Advances in Applied Mathematics

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。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.

关 键 词：BAM 神经网络 稳定性 HOPF分岔 时滞 

分 类 号：O17[理学—数学]