Dynamics of a Large-Scale Spiking Neural Network with Quadratic Integrate-and-Fire Neurons.

Weijie Ye

doi:10.1155/2021/6623926

Abstract

Since the high dimension and complexity of the large-scale spiking neural network, it is difficult to research the network dynamics. In recent decades, the mean-field approximation has been a useful method to reduce the dimension of the network. In this study, we construct a large-scale spiking neural network with quadratic integrate-and-fire neurons and reduce it to a mean-field model to research the network dynamics. We find that the activity of the mean-field model is consistent with the network activity. Based on this agreement, a two-parameter bifurcation analysis is performed on the mean-field model to understand the network dynamics. The bifurcation scenario indicates that the network model has the quiescence state, the steady state with a relatively high firing rate, and the synchronization state which correspond to the stable node, stable focus, and stable limit cycle of the system, respectively. There exist several stable limit cycles with different periods, so we can observe the synchronization states with different periods. Additionally, the model shows bistability in some regions of the bifurcation diagram which suggests that two different activities coexist in the network. The mechanisms that how these states switch are also indicated by the bifurcation curves.

Highlights

Neurons and neural circuits can be modelled as nonlinear dynamical systems to simulate various brain activities
The corresponding mean-field firing rates re and ri are at the quiescence states which are consistent with the network model firing rates (Figures 1(b) and 1(d))
The activity of the mean-field model was verified to be consistent with the activity of the network model

Summary

Introduction

Neurons and neural circuits can be modelled as nonlinear dynamical systems to simulate various brain activities. Brunel and Wang built a working memory network and reduced it to a mean-field model to research the computational mechanisms of how the brain stored the information temporarily [10]. They found that working memory was based on the bistability of the network where one stable state represents the memory activity and the other stable state denotes the spontaneous activity. Once an external stimulus input, the network changed from the spontaneous activity to the ongoing memory activity, indicating that the information of the stimulus has Neural Plasticity been remembered This kind of bistability dynamics has been observed in the decision-making function. Different networks in visual processing [13,14,15,16], neural disease [17,18,19], and movement [20] have been researched by mean-field dynamics

Methods

Results

Conclusion