First-order route to antiphase clustering in adaptive simplicial complexes

Abstract

This Letter investigates the transition to synchronization of oscillator ensembles encoded by simplicial complexes in which pairwise and higher-order coupling weights adapt with time through the Hebbian learning mechanism. These concurrently evolving disparate adaptive coupling weights lead to a novel phenomenon in that the in-phase synchronization is completely obliterated; instead, the anti-phase synchronization is originated. Besides this, the onsets of anti-phase synchronization and desynchronization are manageable through both dyadic and triadic Hebbian 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 would help to understand the underlying synchronization behavior of a range of real-world systems, such as the brain functions and social systems where interactions evolve with time.