中文摘要：

周期性的神经网络(RNN ) 的动力学分析是一第一并且为他们的任何实际应用的必要的步。在现在的纸，容易验证的定理被发现到同样肯定为有在一个判别式矩阵由网络定义的批评条件下面印射的设计的通用 RNN 模型的 asymptotical 稳定性是半积极的明确。这里给的结果不仅在存在之上深深地改善在文学的相关批评以及非批评的动力学结论，而且罐头直接在 RNN 的实际申请被使用。

英文摘要：

The dynamics anMysis of recurrent neural networks （RNNs） is a first and necessary step for any practical applications of them. In the present paper, the easily verified theorem is found to ascertain the asymptotical stability for generic RNN model with projection mapping under the critical condition that a discriminant matrix defined by the networks is semi-positive definite. The results given here not only improve deeply upon the existing relevant critical as well as non-critical dynamics conclusions in literature, but also can be used in the practical application of RNNs directly.