神经网络的分叉理论设计方法

本文用分叉理论的规范形方程设计和综合期望贮存静、动态记忆模式的神经网络。对于期望贮存静态记忆模式的网络，该规范形方程为叉形分叉的；若期望贮存的记忆模式是周期振荡形式，该规范形方程为高余维数Ｈｏｐｆ分叉的，由满足设计约束的规范形系数得到的突触连接系数可以保证期望贮存的记忆模式都能成功地存贮于所设计的网络，且是网络仅有的吸引子，没有伪吸引子，吸引域的范围足够大。

BIFURCATION THEORY METHODS IN THE DESIGN OF ANALOG NEURAL NETWORKS

Normal form equations in bifurcation theory are used to design and syn-thesize analog neural networks which can store st at ic or oscillating memory patterns.For the network storing static memory patterns,the normal form equations are of the pitch- fork bifurcation type. If the stored patterns are periodically oscillating, the normal form equations are of the mutiple Hopf bifurcation type. The synaptic weights obtained from the coefficients of the normal form equations which satisfy the designing restraints can assure the desired memory patterns to be stored in the designed neural network.These pat terns are the networy's stable attractors.There are no spurious attractors.The regime of bassins of attraction is large enough.