具有扩散影响的Hopfield型神经网络的全局渐近稳定性  

Global Asymptotic Stability for Hopfield-Type Neural Networks With Diffusion Effects

作　　者：颜向平[1] 李万同[2] 李继彬 

机构地区：[1]兰州交通大学数学系,兰州730070 [2]兰州大学数学与统计学院,兰州730000

出　　处：《应用数学和力学》2007年第3期328-334,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10571078);甘肃省自然科学基金资助项目(3ZX062-B25-012)

摘　　要：对具有扩散影响的Hopfield型神经网络平衡点的存在唯一性和全局渐近稳定性进行了研究.在激活函数单调非减、可微且关联矩阵和Liapunov对角稳定矩阵有关时,利用拓扑度理论得到了系统平衡点存在的充分条件.通过构造适当的平均Liapunov函数,分析了系统平衡点的全局渐近稳定性.所得结论表明系统的平衡点(如果存在)是全局渐近稳定的而且也蕴含着系统的平衡点的唯一性.The existence, uniqueness and global asymptotic stability of the equilibrium for Hopfieldtype neural networks with diffusion were discussed. The sufficient conditions of the existence and uniqueness of the equilibrium of the system were obtained by applying the topological degree theory when the activation functions are monotonous non-decreasing and differential, and the interconnected matrix is related to the Lianupov diagonal stable matrix. By constructing the average Liapunov functions, the global asymptotic stability of the equilibrium of the system was obtained.

关 键 词：扩散 HOPFIELD型神经网络 平衡点 全局渐近稳定性 

分 类 号：O175[理学—数学]