Synchronization of R{\"o}ssler Oscillators on Scale-free Topologies

TL;DR

This paper investigates how the structure of scale-free networks influences the synchronization of chaotic Rössler oscillators, highlighting the importance of loops and shortest path distributions in achieving synchronization.

Contribution

It demonstrates the critical role of network topology, especially loops and path lengths, in the synchronization behavior of coupled chaotic oscillators on scale-free networks.

Findings

Loops facilitate synchronization in the network.

Tree-like topologies hinder synchronization beyond a certain size.

Shortcuts and path length distribution significantly impact synchronization.

Abstract

We study the synchronization of R{\"o}ssler oscillators as prototype of chaotic systems, when they are coupled on scale-free complex networks. We find that the underlying topology crucially affects the global synchronization properties. Especially, we show that the existence of loops facilitates the synchronizability of the system, whereas R\"ossler oscillators do not synchronize on tree-like topologies beyond a certain size. By considering Cayley trees, modified by various shortcuts, we find that also the distribution of shortest path lengths between two oscillators plays an important role for the global synchronization.