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This paper studies a dynamical system that models the free recall dynamics ofworking memory. This model is a modular neural network with n modules, namedhypercolumns, and each module consists of m minicolumns. Under mild conditionson the connection weights between minicolumns, we investigate the long-termevolution behavior of the model, namely the existence and stability ofequilibriums and limit cycles. We also give a critical value in which Hopfbifurcation happens. Finally, we give a sufficient condition under which thismodel has a globally asymptotically stable equilibrium with synchronizedminicolumn states in each hypercolumn, which implies that in this caserecalling is impossible. Numerical simulations are provided to illustrate ourtheoretical results. A numerical example we give suggests that patterns can bestored in not only equilibriums and limit cycles, but also strange attractors(or chaos).

Steady state behavior of the free recall dynamics of working memory