2022/09/22 by Tianhao Li, Zhixin Liu, Li, Tianhao +4
Biochemistry, Genetics and Molecular Biology · Computer Science · Neuroscience · #FOS: Electrical engineering #Neural Networks and Applications #Neural dynamics and brain function #Receptor Mechanisms and Signaling #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2209.11014
openalex publication_date 2022/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).