A synthesis method based on stability analysis for complex-valued Hopfield neural network

This paper discusses the synthesis problem for a class of discrete time complex-valued Hopfield neural network. To be an associative memory, each memory pattern of the network should be stable and attractive. For this reason, this paper firstly analysis the stability of network, where a generalized Hamming distance defined in complex-valued domain is used to be Lyapunov function. Thus a stable criterion about network parameters is derived and utilized to decide whether the network synthesized by equilibrium equations is local asymptotically stable. If not, then the gain of activation function is regulated until the stable criterion is satisfied. Compared with commonly used Hebb rule, the proposed complex-valued network synthesis method need not orthogonal relations between the set of memory patterns, or the symmetric assumption for the interconnection matrix, but can guarantee each desired memory pattern is attractive.