Synchronization of an evolving complex hyper-network

TL;DR

This paper introduces a new evolving hyper-network model, analyzes its degree distribution, and investigates synchronization phenomena within it, providing new insights into complex system dynamics.

Contribution

It proposes a novel evolving hyper-network model with a joint degree concept and derives synchronization criteria for coupled dynamical systems on hyper-networks.

Findings

Hyper-degree distribution follows a power law.

Synchronization criteria are established based on joint degree matrix.

Numerical examples validate the theoretical results.

Abstract

In this paper, the synchronization in a hyper-network of coupled dynamical systems is investigated for the first time. An evolving hyper-network model is proposed for better describing some complex systems. A concept of joint degree is introduced, and the evolving mechanism of hyper-network is given with respect to the joint degree. The hyper-degree distribution of the proposed evolving hyper-network is derived based on a rate equation method and obeys a power law distribution. Furthermore, the synchronization in a hyper-network of coupled dynamical systems is investigated for the first time. By calculating the joint degree matrix, several simple yet useful synchronization criteria are obtained and illustrated by several numerical examples.