Steady State Behavior of the Free Recall Dynamics of Working Memory

LI Tianhao, LIU Zhixin, LIU Lizheng, HU Xiaoming

系统科学与复杂性(英文) ›› 2024, Vol. 37 ›› Issue (6) : 2424-2450.

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系统科学与复杂性(英文) ›› 2024, Vol. 37 ›› Issue (6) : 2424-2450. DOI: 10.1007/s11424-024-3154-8

Steady State Behavior of the Free Recall Dynamics of Working Memory

    LI Tianhao1,2, LIU Zhixin1,2, LIU Lizheng3, HU Xiaoming4
作者信息 +

Steady State Behavior of the Free Recall Dynamics of Working Memory

    LI Tianhao1,2, LIU Zhixin1,2, LIU Lizheng3, HU Xiaoming4
Author information +
文章历史 +

摘要

This paper studies a dynamical system that models the free recall dynamics of working memory. This model is an attractor neural network with n modules, named hypercolumns, and each module consists of m minicolumns. Under mild conditions on the connection weights between minicolumns, the authors investigate the long-term evolution behavior of the model, namely the existence and stability of equilibria and limit cycles. The authors also give a critical value in which Hopf bifurcation happens. Finally, the authors give a sufficient condition under which this model has a globally asymptotically stable equilibrium consisting of synchronized minicolumn states in each hypercolumn, which implies that in this case recalling is impossible. Numerical simulations are provided to illustrate the proposed theoretical results. Furthermore, a numerical example the authors give suggests that patterns can be stored in not only equilibria and limit cycles, but also strange attractors (or chaos).

Abstract

This paper studies a dynamical system that models the free recall dynamics of working memory. This model is an attractor neural network with n modules, named hypercolumns, and each module consists of m minicolumns. Under mild conditions on the connection weights between minicolumns, the authors investigate the long-term evolution behavior of the model, namely the existence and stability of equilibria and limit cycles. The authors also give a critical value in which Hopf bifurcation happens. Finally, the authors give a sufficient condition under which this model has a globally asymptotically stable equilibrium consisting of synchronized minicolumn states in each hypercolumn, which implies that in this case recalling is impossible. Numerical simulations are provided to illustrate the proposed theoretical results. Furthermore, a numerical example the authors give suggests that patterns can be stored in not only equilibria and limit cycles, but also strange attractors (or chaos).

关键词

Asymptotic stability / bifurcation / free recall / strange attractor / working memory

Key words

Asymptotic stability / bifurcation / free recall / strange attractor / working memory

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LI Tianhao, LIU Zhixin, LIU Lizheng, HU Xiaoming. Steady State Behavior of the Free Recall Dynamics of Working Memory. 系统科学与复杂性(英文), 2024, 37(6): 2424-2450 https://doi.org/10.1007/s11424-024-3154-8
LI Tianhao, LIU Zhixin, LIU Lizheng, HU Xiaoming. Steady State Behavior of the Free Recall Dynamics of Working Memory. Journal of Systems Science and Complexity, 2024, 37(6): 2424-2450 https://doi.org/10.1007/s11424-024-3154-8

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基金

This work was supported by the National Key R&D Program of China under Grant No. 2018YFA0703800, the Natural Science Foundation of China under Grant No. T2293770, the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No. XDA27000000, and Shanghai Municipal Science and Technology Major Project under Grant No. 2021SHZDZX0103.
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