SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 1158-1176, January 2021.
The synchronization of different brain regions is widely observed under both normal and pathological conditions, such as epilepsy. However, the relationship between the dynamics of these brain regions, the connectivity between them, and the ability to synchronize remains an open question. We investigate the problem of inter-region synchronization in networks of Wilson--Cowan/neural field equations with homeostatic plasticity, each of which acts as a model for an isolated brain region. We consider arbitrary connection profiles with only one constraint: the rows of the connection matrices are all identically normalized. We found that these systems often synchronize to the solution obtained from a single, self-coupled neural region. We analyze the stability of this solution through a straightforward modification of the master stability function (MSF) approach and found that synchronized solutions lose stability for connectivity matrices when the second largest positive eigenvalue is sufficiently large for values of the global coupling parameter that are not too large. This result was numerically confirmed for ring systems and lattices and was also robust to small amounts of heterogeneity in the homeostatic set points in each node. Finally, we tested this result on connectomes obtained from 196 subjects over a broad age range (4--85 years) from the Human Connectome Project. We found that the second largest eigenvalue tended to decrease with age, indicating an increase in synchronizability that may be related to the increased prevalence of epilepsy with advancing age.

中文翻译：

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归一化的连接组通过其第二大特征值显示出与年龄的增加的同步性

SIAM Journal on Applied Dynamical Systems，第 20 卷，第 2 期，第 1158-1176 页，2021 年 1 月。
不同大脑区域的同步在正常和病理条件下都被广泛观察到，例如癫痫。然而，这些大脑区域的动态、它们之间的连通性以及同步能力之间的关系仍然是一个悬而未决的问题。我们研究了具有稳态可塑性的 Wilson--Cowan/神经场方程网络中的区域间同步问题，每个方程都充当孤立大脑区域的模型。我们考虑只有一个约束的任意连接配置文件：连接矩阵的行都是相同的归一化。我们发现这些系统通常与从单个自耦合神经区域获得的解决方案同步。我们通过对主稳定性函数 (MSF) 方法的直接修改来分析该解的稳定性，发现当第二大正特征值对于全局耦合参数的值足够大时，同步解会失去连接矩阵的稳定性大。这一结果在环系统和晶格中得到了数值证实，并且对于每个节点中稳态设定点的少量异质性也具有鲁棒性。最后，我们在从人类连接组计划的广泛年龄范围（4--85 岁）的 196 名受试者中获得的连接组上测试了这一结果。我们发现第二大特征值往往随着年龄的增长而降低，表明同步性的增加可能与癫痫患病率随着年龄的增长而增加有关。