School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China.
Big data and Educational Statistics Application Laboratory, Guangdong University of Finance and Economics, Guangzhou 510320, China.
Neural Plast. 2021 Feb 23;2021:6623926. doi: 10.1155/2021/6623926. eCollection 2021.
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.
由于大规模尖峰神经网络的高维复杂性，研究其网络动态较为困难。在过去几十年中，平均场近似已成为降低网络维度的一种有用方法。在本研究中，我们构建了一个具有二次积分和点火神经元的大规模尖峰神经网络，并将其简化为一个平均场模型，以研究网络动态。我们发现，平均场模型的活动与网络活动一致。基于这种一致性，我们对平均场模型进行了双参数分岔分析，以了解网络动态。分岔情况表明，网络模型具有静止状态、具有相对较高点火率的稳定状态和同步状态，分别对应于系统的稳定节点、稳定焦点和稳定周期。存在多个具有不同周期的稳定周期，因此我们可以观察到具有不同周期的同步状态。此外，该模型在分岔图的某些区域显示出双稳性，这表明网络中存在两种不同的活动。分岔曲线还指出了这些状态如何切换的机制。
