Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
Chaos. 2023 Jul 1;33(7). doi: 10.1063/5.0152942.
A potential issue of interest is figuring out how the combination of temporal and higher-order interactions influences the collective dynamics of the brain, specifically, neuronal synchronization. Motivated by this, here we consider an ensemble of neurons interacting with each other through gap junctions, modeled by temporal higher-order networks (simplicial complexes), and study the emergence of complete neuronal synchronization. We find that the critical synaptic strength for achieving neuronal synchronization with time-varying higher-order interaction is relatively lower than that with temporal pairwise interactions or static many-body interactions. Our study shows that neuronal synchronization can occur even in the sole presence of higher-order, time-varying interactions. We also find that the enhancement in neuronal synchronization in temporal higher-order structure is highly related to the density of group interactions among the neurons. Furthermore, to characterize the local stability of the synchronous solution, we use the master stability function approach, which shows that the numerical findings are in good agreement with the analytically derived conditions.
一个可能引起关注的问题是，弄清楚时间和高阶相互作用的组合如何影响大脑的集体动力学，特别是神经元同步。受此启发，我们在这里考虑通过间隙连接相互作用的神经元集合，通过时间高阶网络（单纯复形）进行建模，并研究完全神经元同步的出现。我们发现，实现具有时变高阶相互作用的神经元同步的临界突触强度相对低于具有时变成对相互作用或静态多体相互作用的临界突触强度。我们的研究表明，即使仅存在高阶时变相互作用，也可以发生神经元同步。我们还发现，时间高阶结构中神经元同步的增强与神经元之间的群体相互作用的密度密切相关。此外，为了描述同步解的局部稳定性，我们使用主稳定性函数方法，该方法表明数值结果与分析得出的条件非常吻合。
