Analysis of free recall dynamics of an abstract working memory model

This paper analyzes the free recall dynamics of a working memory model. Free recalling is the reactivation of a stored pattern in the memory in the absence of the pattern. Our free recall model is based on an abstract model of a modular neural network composed on $N$ modules, hypercolumns, each of which is a bundle of minicolumns. This paper considers a network of $N$ modules, each consisting of two minicolumns, over a complete graph topology. We analyze the free recall dynamics assuming a constant, and homogeneous coupling between the network modules. We obtain a sufficient condition for synchronization of network's minicolumns whose activities are positively correlated. Furthermore, for the synchronized network, the bifurcation analysis of one module is presented. This analysis gives a necessary condition for having a stable limit cycle as the attractor of each module. The latter implies recalling a stored pattern. Numerical results are provided to verify the theoretical analysis.