Contrarians synchronize beyond the limit of pairwise interactions

TL;DR

This paper demonstrates that higher-order interactions in multi-dimensional Kuramoto oscillators can induce collective synchronization even with negative coupling, revealing new dynamical states beyond pairwise interactions.

Contribution

It provides an exact solution showing how multi-dimensional higher-order interactions lead to synchronization and symmetry breaking in contrarian oscillator populations.

Findings

Higher-order interactions induce synchronization with negative coupling.

Existence of a frequency-locked state with two distinct phase clusters.

Exact microscopic dynamics solution for forward and backward transitions.

Abstract

We give evidence that a population of pure contrarians globally coupled D-dimensional Kuramoto oscillators reaches a collective synchronous state when the interplay between the units goes beyond the limit of pairwise interactions. Namely, we will show that the presence of higher order interactions may induce the appearance of a coherent state even when the oscillators are coupled negatively to the mean field. An exact solution for the description of the microscopic dynamics for forward and backward transitions is provided, which entails imperfect symmetry breaking of the population into a frequency-locked state featuring two clusters of different instantaneous phases. Our results contribute to a better understanding of the powerful potential of group interactions entailing multi-dimensional choices and novel dynamical states in many circumstances, such as in social systems.