Critical phenomenon of two coupled phase oscillators

Measure synchronization (MS) is a novel phenomenon which can be found in some coupled Hamiltonian systems (HS). In this paper, we built a new model called two coupled phase oscillators system (CPOS), and found that, under the appropriate initial conditions, it will meet a critical phenomenon in the phase space as the coupling strength increases. We also found the critical state by introducing the Poincaré section technique. We established a new formula for the critical coupling strength by analyzing the HS model, and extended this formula to the CPOS. The numerically analytical results show the reason why the measure synchronization of CPOS does not exist.