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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．
An important property of the discrete Hopfield neural network is that it can always converge to a steady state under the asynchronous operation mode and always converge to a limit cycle whose period does not exceed 2 under the synchronous operation mode. It is the model can be used for associative memory design, combinatorial optimization theory. In this paper, the convergence theorem of delayed discrete Hopfield networks is given. Under the asynchronous operation mode, the convergence theorem of symmetric connection weight matrix is proved, the convergence result of the existing discrete Hop-field network is generalized, and the stability of maximum energy point and delayed discrete Hopfield network is given. State and evolutionary characteristics of the steady state neighborhood, the coordination relationship between energy function convergence and network stability during asynchronous operation is obtained.