The dynamics of selective recall in an associative memory model are analyzed in the scenario of one-to-many association. One-to-many association is one of the most important characteristics of our memory system because a homophone, for example, associates with more than one word and each word can have several meanings. The present model, which can deal with one-to-many association, consists of a heteroassociative network and an autoassociative network. In the heteroassociative network, a mixture of associative items in one-to-many association is recalled by a key item. In the autoassociative network, the selective recall of one of the associative items is examined by providing a seed of a target item either to the heteroassociative network (Model 1) or to the autoassociative network (Model 2). We show by both simulation studies and theoretical analysis that the critical similarity of Model 2 is not sensitive to the change in the dimension ratio of key vectors to associative vectors, and it has smaller critical similarity (correlation between the seed and the target item) than Model 1 for a large initial overlap. On the other hand, we show that Model 1 has smaller critical similarity for a small initial overlap.
We also show that unreachable equilibrium states exist in the proposed model. There is a critical loading rate $\alpha_r$ where the reachable equilibrium states are disappeared. Above the critical loading rate $\alpha_r$, which is smaller than the storage capacity $\alpha_c$, all equilibrium states are stable, but cannot be reached.