Analysis and synthesis for a class of complex-valued associative memories

In this paper we consider a class of complex-valued Hopfield neural network which is a complex value extension of the real-valued Hopfield type neural network. To apply it to complex-valued associative memory (i.e. to store each desired memory as equilibrium of the network) we design a synthesis method. Neither the orthogonal relations between the set of memory patterns nor the symmetric assumption for the interconnection matrix is needed in the synthesis section. The stability analysis based on Lyapunov function is utilized to guarantee each desired memory is attractive.