Synchronization in adaptive higher-order networks

TL;DR

This paper introduces a framework for understanding synchronization in adaptive higher-order networks, highlighting how group interactions and adaptivity influence the emergence and stability of synchronized states.

Contribution

It develops a general theoretical framework for adaptive higher-order networks, extending beyond pairwise interactions, and analyzes conditions for stable synchronization.

Findings

Global synchronization can occur in adaptive higher-order networks.

Necessary conditions for stability relate to the master stability function.

Group interactions and adaptivity can induce transitions between synchronized and desynchronized states.

Abstract

Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they focus solely on pairwise interactions. In this study, we employ adaptive higher-order networks to describe these systems by proposing a general framework incorporating both adaptivity and group interactions. We demonstrate that global synchronization can exist in those complex structures, and we provide the necessary conditions for the emergence of a stable synchronous state. Additionally, we analyzed some relevant settings, and we showed that the necessary condition is strongly related to the master stability equation, allowing to separate the dynamical and structural properties. We illustrate our theoretical findings through examples involving adaptive higher-order networks of coupled generalized Kuramoto oscillators with phase lag. We also show that the interplay of group interactions and adaptive connectivity results in the formation of stability regions that can induce transitions between synchronization and desynchronization