Synchronization in Random Geometric Graphs

TL;DR

This paper investigates synchronization in random geometric graphs, revealing that they synchronize more easily but have less stable fully synchronized states compared to other networks, and proposes rewiring to improve stability.

Contribution

It provides new insights into synchronization behavior in random geometric graphs and introduces a rewiring method to enhance stability and reduce required coupling strength.

Findings

Synchronization onset is similar to that in random graphs of same size.

Fully synchronized states are less stable in geometric graphs.

Rewiring improves stability and lowers coupling threshold.

Abstract

In this paper we study the synchronization properties of random geometric graphs. We show that the onset of synchronization takes place roughly at the same value of the order parameter that a random graph with the same size and average connectivity. However, the dependence of the order parameter with the coupling strength indicates that the fully synchronized state is more easily attained in random graphs. We next focus on the complete synchronized state and show that this state is less stable for random geometric graphs than for other kinds of complex networks. Finally, a rewiring mechanism is proposed as a way to improve the stability of the fully synchronized state as well as to lower the value of the coupling strength at which it is achieved. Our work has important implications for the synchronization of wireless networks, and should provide valuable insights for the development and deployment of more efficient and robust distributed synchronization protocols for these systems.