First-order route to antiphase clustering in adaptive simplicial complexes

TL;DR

This paper explores how adaptive higher-order interactions in simplicial complexes lead to antiphase synchronization, with potential implications for understanding dynamic systems like brains and social networks.

Contribution

It introduces a novel adaptive mechanism for simplicial complexes that results in antiphase synchronization, expanding understanding of complex system dynamics.

Findings

Adaptive coupling weights induce antiphase synchronization.

Synchronization and desynchronization can be controlled via learning rates.

Theoretical validation using Ott-Antonsen reduction confirms numerical results.

Abstract

This Letter investigates the transition to synchronization of oscillator ensembles encoded by simplicial complexes in which pairwise and higher-order coupling weights alter with time through a rate-based adaptive mechanism inspired by the Hebbian learning rule. These simultaneously evolving disparate adaptive coupling weights lead to a phenomenon in which the in-phase synchronization is completely obliterated; instead, the anti-phase synchronization is originated. In addition, the onsets of antiphase synchronization and desynchronization are manageable through both dyadic and triadic learning rates. The theoretical validation of these numerical assessments is delineated thoroughly by employing Ott-Antonsen dimensionality reduction. The framework and results of the Letter could help in the understanding of the underlying synchronization behavior of a range of real-world systems, such as brain functions and social systems where interactions evolve with time.