A type of two-degree-of-freedom vibration system with bilateral nonlinear constraints is established. Through the fourth-order Runge-Kutta numerical algorithm, the dynamic characteristics of the p/1 periodic motion of the system under low frequency excitation, the law of mutual transition and the corresponding law of the coexistence zone of gap and period are analyzed. The cell mapping method is used to study the distribution law of different attractors and attracting domains in the coexistence area of periodic motion. The results show that the periodic motions of the system are mainly transferred through Grazing bifurcation and Saddle-node bifurcation. Due to the irreversible transition process, there is a coexistence zone of periodic motion between adjacent motions. As the gap increases, the range of the coexistence zone of periodic motion of the system gradually decreases.