# Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices

## TL;DR

This paper investigates the complex collective dynamics of coupled phase oscillators with three-way interactions, revealing abrupt desynchronization transitions and extensive multistability, which are relevant for understanding systems like the human brain.

## Contribution

It introduces a novel analysis of simplicial interactions in oscillator systems, uncovering unique phenomena such as continuum desynchronization and infinite multistability.

## Key findings

- Discovered abrupt desynchronization transitions without synchronization counterparts.
- Identified extensive multistability with infinitely many stable states.
- Highlighted implications for systems like the human brain and social networks.

## Abstract

Collective behavior in large ensembles of dynamical units with non-pairwise 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.