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arXiv · 2209.11014

Steady state behavior of the free recall dynamics of working memory

Tianhao Li·Zhixin Liu·Lizheng Liu·Xiaoming Hu
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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).

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Tianhao Li, Zhixin Liu, Lizheng Liu, Xiaoming Hu. 2022-09-22. Steady state behavior of the free recall dynamics of working memory. https://arxiv.org/abs/2209.11014

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