判定离散Hopfield神经网络稳定性的新方法

判定离散Hopfield神经网络稳定性的新方法 The New Criterions on Stability of Discrete Time Hopfield Neural Networks 高莹 GAO Ying 1 1 2 3 first-author 熊志欢 XIONG Zhi huan 2 1 2 3 武汉大学数学与统计学院 武汉大学数学与统计学院 School of Mathematics and Statistics, Wuhan Univerisity School of Mathematics and Statistics, Wuhan Univerisity 北京理工大学自动控制系,湖北,武汉,430072 北京理工大学自动控制系,湖北,武汉,430072 Department of Automatic Control, Beijing University of Science and Technology Department of Automatic Control, Beijing University of Science and Technology ,北京,100081 ,北京,100081 寻求判断离散 Hopfield神经网络稳定性的新判据 .具体考虑神经元的权值矩阵元素和阀值之间的关系 ,依此判断能量函数的收敛性 ,得到了一个与阀值无关、不需权值矩阵对称的新判据 ;在新判据的基础上作出数学变形和分析 ,并用线性方程的解去刻划稳定点的存在性 ,得到了稳定点存在的一个充要条件 .最后将离散Hopfield神经网络的稳定点存在问题转化为在有限区域内连续函数的零点解的问题 To study the new criterion on stability of the discrete time Hopfield neural networks. The paper considered the connection between entries of weight matrices and thresholds of neurons to decide the convergence of energy functions, and derived a new criterion independent of the thresholds and the symmetry of weight matrices; then made rigorous mathematical calculations on this; and gave a sufficient and necessary condition for the existence of stable points via solutions of a linear equation. Finally, the existence question of the equilibrium solutions was turned into that of the zero solutions of the continuous functions. Hopfield神经网络 稳定性 稳定点 Hopfield neural networks stability stable points TP183 国家基础科学发展计划 （ 973计划 ）资助 2002-01-01 2021-04-01 1