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关于Ｈｏｐｆｉｅｌｄ网的状态转移轨迹、吸引子、吸引域和如何逃离局部极小点等问题，尤其是对具有一般权系数和偏置的网络，一直没有得到很好的解决．本文首先定义了Ｈｏｐｆｉｅｌｄ网的关联网络，分析了关联网络的性质，找出了具有关联关系的网络状态转移轨迹之间存在的关联关系和规律．从而，如果已知了一个网络的状态转移轨迹，利用这一规律可以很容易地得出与其相关联的网络的状态转移轨迹，并给出了它们的吸引子之间关系的结论，为Ｈｏｐｆｉｅｌｄ网络的局部极小点的逃离、最不容错网络的判断提供了方法，为对网络的进一步分析和设计提供了一种新的方法和途径．所进行的大量计算机仿真实验验证了这一规律的存在．
On Hopfield network state transition trajectory, attractors, attracting domain and how to escape from local minima and other issues, especially for the network with general weighting coefficient and bias, has not been well solved. In this paper, we firstly define the network of Hopfield network, analyze the properties of the network and find out the relationship and rules between the network state transition trajectories. Therefore, if a state transition trajectory of a network is known, the state transition trajectories of the networks associated with it can be easily obtained by using this law, and the conclusion of the relationship between their attractors is given. This is a Hopfield network The method of judging the most imperfect network provides a new method and way for the further analysis and design of the network. A large number of computer simulation experiments verify the existence of this law.