Transitions to Measure Synchronization in Coupled Hamiltonian Systems

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.