Steady state behavior of the free recall dynamics of working memory

TL;DR

This paper analyzes a neural network model of working memory's free recall, exploring its long-term behavior, stability, bifurcations, and the conditions leading to synchronized or chaotic states, supported by numerical simulations.

Contribution

It provides a mathematical analysis of the stability and bifurcation phenomena in a neural model of working memory, including conditions for synchronization and chaos.

Findings

Existence and stability of equilibriums and limit cycles.

Identification of Hopf bifurcation points.

Conditions for globally stable synchronized states.

Abstract

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).