Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark.
Chaos. 2021 Feb;31(2):023141. doi: 10.1063/5.0031630.
We study the macroscopic dynamics of large networks of excitable type 1 neurons composed of two populations interacting with disparate but symmetric intra- and inter-population coupling strengths. This nonuniform coupling scheme facilitates symmetric equilibria, where both populations display identical firing activity, characterized by either quiescent or spiking behavior, or asymmetric equilibria, where the firing activity of one population exhibits quiescent but the other exhibits spiking behavior. Oscillations in the firing rate are possible if neurons emit pulses with non-zero width but are otherwise quenched. Here, we explore how collective oscillations emerge for two statistically identical neuron populations in the limit of an infinite number of neurons. A detailed analysis reveals how collective oscillations are born and destroyed in various bifurcation scenarios and how they are organized around higher codimension bifurcation points. Since both symmetric and asymmetric equilibria display bistable behavior, a large configuration space with steady and oscillatory behavior is available. Switching between configurations of neural activity is relevant in functional processes such as working memory and the onset of collective oscillations in motor control.
我们研究了由两个相互作用的种群组成的大网络的宏观动力学，这些种群具有兴奋性类型 1 神经元，具有不同但对称的内群和群间耦合强度。这种非均匀的耦合方案有利于对称平衡，其中两个种群都表现出相同的放电活动，表现为静止或脉冲行为，或者不对称平衡，其中一个种群的放电活动表现为静止，但另一个种群表现为脉冲行为。如果神经元发射具有非零宽度的脉冲但其他方面被抑制，则可能会出现放电率的振荡。在这里，我们探索了当神经元数量趋于无穷大时，两个统计上相同的神经元种群的集体振荡是如何出现的。详细分析揭示了集体振荡是如何在各种分岔情景中产生和破坏的，以及它们是如何围绕更高的余维分岔点组织的。由于对称和不对称平衡都表现出双稳态行为，因此存在具有稳定和振荡行为的大配置空间。在工作记忆等功能过程以及运动控制中集体振荡的发生之间的神经活动配置之间进行切换是相关的。
