Synchronizability and synchronization dynamics of weighed and unweighed scale free networks with degree mixing

摘要

We study the synchronizability and the synchronization dynamics of networksof nonlinear oscillators. We investigate how the synchronization of the networkis influenced by some of its topological features such as variations of thepower law exponent $\gamma$ and the degree correlation coefficient $r$. Usingan appropriate construction algorithm based on clustering the network verticesin $p$ classes according to their degrees, we construct networks with anassigned power law distribution but changing degree correlation properties. Wefind that the network synchronizability improves when the network becomesdisassortative, i.e. when nodes with low degree are more likely to be connectedto nodes with higher degree. We consider the case of both weighed and unweighednetworks. The analytical results reported in the paper are then confirmed by aset of numerical observations obtained on weighed and unweighed networks ofnonlinear R\"ossler oscillators. Using a nonlinear optimization strategy wealso show that negative degree correlation is an emerging property of networkswhen synchronizability is to be optimized. This suggests that negative degreecorrelation observed experimentally in a number of physical and biologicalnetworks might be motivated by their need to synchronize better.