Structural characterization of oscillations in brain networks with rate dynamics
Structural characterization of oscillations in brain networks with rate dynamics
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具有速率动力学的脑网络振荡的结构表征
DOI：
10.1016/j.automatica.2022.110653
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发表时间：
2022
期刊：
影响因子：
6.4
通讯作者：
Cortés, Jorge
中科院分区：
文献类型：
--
作者：
Nozari, Erfan;Planas, Robert;Cortés, Jorge
在大脑表现出的多种动态活动模式中，振荡是最显着和最广泛研究的形式之一，但仍远未得到充分理解。在本文中，我们使用称为线性阈值动力学的中尺度大脑活动的经典神经质量模型，提供了神经网络中振荡行为存在的各种结构特征。利用这种动力学的切换仿射性质，我们获得了网络结构及其外部输入存在振荡的各种必要和/或充分条件：（i）二维兴奋-抑制网络（E-I对），（ii）具有一个抑制但任意数量的兴奋节点的网络，（iii）具有任意数量节点的纯抑制网络，以及（iv）E-I对网络。在我们的整个治疗过程中，考虑到所考虑的动力学的任意维度，我们依靠稳定平衡的缺乏作为振荡存在的基于系统的代理，并提供广泛的数值结果来支持其与计算神经科学中更标准的、基于信号的振荡定义的紧密关系。
Among the versatile forms of dynamical patterns of activity exhibited by the brain, oscillations are one of the most salient and extensively studied, yet are still far from being well understood. In this paper, we provide various structural characterizations of the existence of oscillatory behavior in neural networks using a classical neural mass model of mesoscale brain activity called linear-threshold dynamics. Exploiting the switched-affine nature of this dynamics, we obtain various necessary and/or sufficient conditions on the network structure and its external input for the existence of oscillations in (i) two-dimensional excitatory–inhibitory networks (E-I pairs), (ii) networks with one inhibitory but arbitrary number of excitatory nodes, (iii) purely inhibitory networks with an arbitrary number of nodes, and (iv) networks of E-I pairs. Throughout our treatment, and given the arbitrary dimensionality of the considered dynamics, we rely on the lack of stable equilibria as a system-based proxy for the existence of oscillations, and provide extensive numerical results to support its tight relationship with the more standard, signal-based definition of oscillations in computational neuroscience.