Global synchronization on time-varying higher-order structures

TL;DR

This paper investigates how the evolution of higher-order network structures over time affects the emergence of global synchronization in complex systems, extending existing theoretical frameworks to dynamic hypergraphs and simplicial complexes.

Contribution

It extends the master stability formalism to include the effects of time-varying higher-order structures, providing a general theoretical approach for analyzing synchronization.

Findings

The extended formalism successfully predicts synchronization behavior in dynamic hypergraphs.

Application to Stuart-Landau and Lorenz oscillators validates the theoretical predictions.

Time-varying structures can both facilitate and hinder synchronization depending on their evolution.

Abstract

Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real world applications, the latter are not static but do evolve in time, in this paper we thus discuss the impact of the time-varying nature of high-order structures in the emergence of global synchronization. To achieve this goal we extend the master stability formalism to account, in a general way, for the additional contributions arising from the time evolution of the higher-order structure supporting the dynamical systems. The theory is successfully challenged against two illustrative examples, the Stuart-Landau nonlinear oscillator and the Lorenz chaotic oscillator.