2019/03/31 by Per Sebastian Skardal, Alex Arenas, Àlex Arenas · 5 citations
Computer Science · Engineering · Mathematics · Neuroscience · Physics and Astronomy · #Artificial intelligence #Collective behavior #Combinatorics #Complex system #Computer science #Dynamical systems theory #Mathematics #Multistability #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Phase transition #Physics #Pure mathematics #Quantum mechanics #Simplex #Simplicial approximation theorem #Simplicial complex #Slime Mold and Myxomycetes Research #Statistical physics #Synchronization (alternating current) #Topology (electrical circuits) #nlin.AO
paper · pdf · doi:10.1103/physrevlett.122.248301
published as Phys. Rev. Lett. 122, 248301 (2019)
arxiv created 2019/05/30 · openalex publication_date 2019/06/19 · arxiv updated 2019/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.