Measure Synchronization and Phase Coherence in a High Dimensional Hamiltonian System

Partial and complete measure synchronizations (MSs) are investigated in a high-dimensional Hamiltonian system. Here, a four-coupled ring-shaped rotor model is employed. We calculate the averaged energy of each rotor numerically to address the clustering process of measure synchronization. Poincaré sections are used to analyze the dynamic mechanism of partial MS and complete MS transitions, and the separatrix crossing is revealed to be the dynamical mechanism behind all different MS transition behaviors. By calculating the averaged frequency of each rotor, we explore the relationship between frequency locking and MS, and reveal a one-to-one correspondence. Furthermore, we find that abrupt changes in global or even partial phase coherence between the phase oscillators can be an indicator for MS transitions, albeit full phase coherence is not equivalent to measure synchronization.