Synchronization of Rössler oscillators on scale-free topologies

We study the synchronization of Rössler oscillators as prototypes of chaotic systems on scale-free complex networks. As it turns out, the underlying topology crucially affects the global synchronization properties. In particular, we show that the existence of loops facilitates the synchronizability of the system, whereas Rössler oscillators do not synchronize on tree-like topologies beyond a certain size. Moreover, it is not the mere number of loops that counts for synchronization but also the type of loops. By considering Cayley trees modified by additional loops in different ways, we find out that also the distribution of shortest path lengths between two oscillators plays an important role for the global synchronization.