Neuronal synchronization in time-varying higher-order networks

Abstract

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.

Analysis of the optimal target node to reduce seizure-like discharge in networks

“…[39][40][41] A number of studies have focused on the synchronization behaviors underlying higher-order interactions. For example, high-order interaction can lead to the traveling-wave propagation, [42] enhance the neuronal synchronization, [43] and realize the optimal control on synchronization. [44] These works are of great interest for avoiding pathological synchronization, which highlights considering the higher-order interaction in epilepsy networks is a significant direction in future researches.…”

Global synchronization on time-varying higher-order structures

“…The codes used in the simulations for this article is available openly on Github repository [43]. All other data that support the findings of this study are included within the article.…”

“…By considering the simultaneous interactions of many agents, higher-order structures, namely hypergraphs [19] and simplicial complexes [20], offer a more comprehensive understanding of complex systems. These higher-order structures have been proven to produce novel features in various dynamical processes, including consensus [21,22], random walks [23,24], pattern formation [14,25,26], synchronization [14,[27][28][29][30][31][32], social contagion and epidemics [33,34]. Nevertheless, the suggested framework is not sufficiently general to describe systems with many-body interactions that vary with time.…”

Collective dynamics of swarmalators with higher-order interactions

“…In this context, the impact of higher-order interactions on the domain of synchronization has been the subject of thorough investigation in recent years [55][56][57][58][59][60][61][62][63][64] . These studies have unveiled that the incorporation of higher-order interactions among dynamic units has the potential to give rise to a plethora of new collective phenomena.…”