延迟离散Hopfield型神经网络异步收敛性  

CONVERGENCE OF DISCRETE HOPFIELDTYPE NEURAL NETWORKS WITH TIMEDELAY IN A SERIAL MODE

作　　者：邱深山[1,2] 徐晓飞[1,2] 刘明珠 王亚东[1,2] 

机构地区：[1]哈尔滨工业大学计算机科学与工程系 [2]哈尔滨工业大学数学系

出　　处：《计算机研究与发展》1999年第5期546-552,共7页Journal of Computer Research and Development

基　　金：国家自然科学基金

摘　　要：离散Ｈｏｐｆｉｅｌｄ型神经网络的一个重要性质是异步运行方式下总能收敛到稳定态；同步运行方式下总能收敛到周期不超过２的极限环．它是该模型可以用于联想记忆设计、组合优化计算的理论基础．文中给出了延迟离散Ｈｏｐｆｉｅｌｄ型网络的收敛性定理．在异步运行方式下，证明了对称连接权阵的收敛性定理，推广了已有的离散Ｈｏｐ－ｆｉｅｌｄ型网络的收敛性结果，给出了能量函数极大值点与延迟离散Ｈｏｐｆｉｅｌｄ型网络的稳定态的关系及稳定态邻域的演化特征，得到了能量函数收敛与异步运行时网络达到稳定的协调关系．It is known that an important property of the discrete Hopfield\|type neural network is that it always converges to a stable state when operating in a serial mode and to a cycle of length at most 2 when operating in a full parallel model.These properties are the basis for the potential applications of this model,such as associative memory devices and combinatorial optimization.Convergence theorems of discrete Hopfield\|type neural networks with delay are obtained in the paper.Under a proper assumption,it is proved that any discrete Hopfield\|type neural network with delay will converge to a stable state when operating in the serial mode,and one of the weight matrices is a symmetric one and can generalize convergence theorem in earlier works.The authors also relate maximum of modified energy function to stable state of neural network with delay and obtain evolution features in neighborhood of stable state.In other words,this network can converge to a stable state after one time interval.Accordant relations between convergence of the energy function and stabilization of correspondent network in the serial mode are presented as well.

关 键 词：神经网络 延迟 收敛性 稳定态 HOPFIELD网络 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]