  We investigate synchronization in complex networks of noisy phase
oscillators. We find that, while too weak a coupling is not sufficient for the
whole system to synchronize, too strong a coupling induces a nontrivial type of
phase slip among oscillators, resulting in synchronization failure. Thus, an
intermediate coupling range for synchronization exists, which becomes narrower
when the network is more heterogeneous. Analyses of two noisy oscillators
reveal that nontrivial phase slip is a generic phenomenon when noise is present
and coupling is strong. Therefore, the low synchronizability of heterogeneous
networks can be understood as a result of the difference in effective coupling
strength among oscillators with different degrees; oscillators with high
degrees tend to undergo phase slip while those with low degrees have weak
coupling strengths that are insufficient for synchronization.
