Fixed points of complex-valued bidirectional associative memory

A discrete complex-valued bidirectional associative memory (CVBAM) is considered. The input and output of CVBAM are bipolar complex numbers, of which the two components take the value of either −1 or 1. We prove that the stored patterns are all fixed points of CVBAM provided certain sufficient conditions are satisfied. It is shown that each fixed point belongs to a fixed point group which consists of four fixed points. Supporting numerical results are provided.

► A discrete complex-valued bidirectional associative memory network is considered.
► Sufficient condition is given for stored patterns to be fixed points of the network.
► Each fixed point is shown to belong to a fixed point group of four fixed points.