  Transitions to measure synchronization in two coupled $\phi ^{4}$ lattices
are investigated based on numerical simulations. The relationship between
measure synchronization (MS), phase locking and system's total energy is
studied both for periodic and chaotic states. Two different scalings are
discovered during the process to MS according to phase locking. Random walk
like phase synchronization in chaotic measure synchronization is found, and
phase locking interrupted by phase slips irregularly is also investigated.
Meanwhile, related analysis is qualitative given to explain this phenomenon.
