This paper studies a dynamical system that models the free recall dynamics of
working memory. This model is a modular neural network with n modules, named
hypercolumns, and each module consists of m minicolumns. Under mild conditions
on the connection weights between minicolumns, we investigate the long-term
evolution behavior of the model, namely the existence and stability of
equilibriums and limit cycles. We also give a critical value in which Hopf
bifurcation happens. Finally, we give a sufficient condition under which this
model has a globally asymptotically stable equilibrium with synchronized
minicolumn states in each hypercolumn, which implies that in this case
recalling is impossible. Numerical simulations are provided to illustrate our
theoretical results. A numerical example we give suggests that patterns can be
stored in not only equilibriums and limit cycles, but also strange attractors
(or chaos)