Department of Mathematics, Trinity College, Hartford, Connecticut 06106, USA.
Departament d'Enginyeria Informatica i Matemátiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain.
Phys Rev Lett. 2019 Jun 21;122(24):248301. doi: 10.1103/PhysRevLett.122.248301.
Collective behavior in large ensembles of dynamical units with nonpairwise interactions may play an important role in several systems ranging from brain function to social networks. Despite recent work pointing to simplicial structure, i.e., higher-order interactions between three or more units at a time, their dynamical characteristics remain poorly understood. Here we present an analysis of the collective dynamics of such a simplicial system, namely coupled phase oscillators with three-way interactions. The simplicial structure gives rise to a number of novel phenomena, most notably a continuum of abrupt desynchronization transitions with no abrupt synchronization transition counterpart, as well as extensive multistability whereby infinitely many stable partially synchronized states exist. Our analysis sheds light on the complexity that can arise in physical systems with simplicial interactions like the human brain and the role that simplicial interactions play in storing information.
具有非成对相互作用的大规模动力单元集合中的集体行为可能在从大脑功能到社交网络的多个系统中发挥重要作用。尽管最近的工作指出了单纯形结构，即在一次三个或更多单元之间的高阶相互作用，但它们的动力学特性仍未被很好地理解。在这里，我们分析了这样一个单纯形系统的集体动力学，即具有三向相互作用的耦合相位振荡器。单纯形结构产生了许多新的现象，最显著的是一系列突然去同步的转变，没有对应的突然同步转变，以及广泛的多稳定性，即存在无限多个稳定的部分同步状态。我们的分析揭示了具有单纯形相互作用的物理系统（如人类大脑）中可能出现的复杂性，以及单纯形相互作用在存储信息方面所扮演的角色。
