Dynamics of Higher Order Neural Networks and its Application

在高阶神经网络（HONN）的研究中，我们得到了以下结果。(1)HONN在各种数值模拟方面都上级传统模式。(1-1)HONN在函数逼近、模式识别和时间序列预测方面具有上级的优势，而且每个模型的参数个数与常规模型相同。(1-2)在确定网络结构的情况下，HONN模型优于传统模型，具有上级的优点。(1-3)HONN对序列模式的联想记忆能力优于传统模式，具有上级的特点. (2)对HONN的动力学进行了理论分析。(2-1)从理论上证明了联想记忆中回忆能力的动态变化。(2-2)结果表明，HONN模型在模式分离能力上比传统模型有上级的优势。(3)用神经网络建立了配电线路盐害诊断系统，结果表明，HONN在诊断配电线路盐害方面上级传统的模型。

In this research with higher order neural networks(HONN), we have obtained the following results.(1) HONN are superior in various numerical simulations to the conventional model.(1-1) HONN are superior in function approximation, pattern recognition and prediction of time series by using the same number of parameters of each model to the conventional model.(1-2) In the case of determining the structure of networks, HONN are superior to the conventional model.(1-3) HONN are superior in associative memory of sequential patterns to the conventional model.(2) Theoretical analysis are made with dynamic of HONN.(2-1) Dynamics of recalling ability in associative memory is shown theoretically.(2-2) It is shown that HONN are superior in separation ability of patterns to the conventional model.(3) HONN are superior in separation to the conventional model.Diagnosis systems of injury by salt for distribution lines are constructed by neural networks.It is shown that HONN are superior in this problem to the conventional model.