Transition to measure synchronization in coupled Hamiltonian systems

Abstract

The transition to measure synchronization in two coupled φ4 equations are investigated numerically both for quasiperiodic and chaotic cases. Quantities like the bare energy and phase difference are employed to study the underlying behaviors during this process. For transition between quasiperiodic states, the distribution of phase difference tends to concentrate at large angles before measure synchronization, and is confined to within a certain range after measure synchronization. For transition between quasiperiodicity and chaos, phase locking is not achieved and a random-walk-like behavior of the phase difference is found in the measure synchronized region. The scaling relationship of the phase distribution and the behavior of the bare energy are also discussed.