The influence of degree mixing patterns on synchronization paths

Many real networks display assortative and disassortative degree mixing patterns. In this paper, the impact of assortativity on the ubiquitous synchronizing process is systematically investigated. A rewiring model is adopted to generate networks of various assortativity following the same degree distribution. Numeric simulations of phase synchronization are carried in synthetic assortative networks. By carefully observing the collective dynamics in synchronizing processes, we find that assortative networks are more likely to reach local synchronization than disassortative ones even if they obey identity degree distributions. Moreover, the synchronizing process in assortative and disassortative SF networks show different synchronizing patterns, which are indicated by the merging of equivalent small synchronized clusters and growing of one large synchronized core. In the meanwhile, the assortative pattern affects synchronizing process stronger than disassortative pattern when they deviate from neutral network at the same assortativity degree. Phase synchronizing processes are also carried in assortative and disassortative random networks and results show that degree mixing has little influence, which suggests that the influences of assortativity in SF networks might be attributed to the strong heterogeneous of power-law degree distribution.