一类神经网络模型的解及其渐近性态

Solutions and Asymptotically Stable Behavior of a Neural Network Model

摘要: 通过对简单一维微分方程的求解,得出了一类人工神经网络模型的解解析表达式。它是由对称阵的特征值与特征向量表达。根据此解析表达式推出了该神经网络模型在特殊情况下的解析表达式。在特殊情况下,特征值与特征向量的神经网络计算已有很多论文论及。最后利用解析表达式分析了该神经网络解的渐近稳定性态。

Abstract: In this paper, the differential equation of an artificial neural network model is solved by solving a simple one dimension differential equation.The solutions of the neural network that is obtained are represented by the eigenvalues and eigenvectors of the symmetric matrix.Then the other solutions in special conditions are obtained using the solutions in general conditions.In special condtions,the neural network is employed to compute out all eigenvalues and eigenvectors by many dissertations.Finally,the asymptotic stable behavior is analyzed using the solutions.