Abstract: The respiratory control system precisely regulates the breathing rhythm to adapt to the body's requirements in different physiological and pathological states. Pathological dyspnea can occur when oxygen levels in the arterial blood drop below the standard threshold. The pre-B?tzinger complex serves as a crucial site for the generation of the respiratory rhythm, contains expiratory, inspiratory, and post-inspiratory neurons, which work in collaboration to regulate the respiratory rhythm through a variety of mechanisms, including neural and chemical modulation. Under certain hypoxic conditions, the closed-loop respiratory control system can self-recovery, as demonstrated in this study which investigates the system's self-recovery following sustained hypoxia under different initial conditions. The study demonstrates that the system can recover completely to normoxic level, partially recover to mild hypoxic level or completely fail to recover. Utilizing a simplified model for dynamic analysis based on square wave currents, the study investigates the dynamic mechanisms of the system's different responses. The results indicate that the changes of bifurcation structures at different stages during the sustained hypoxia are key factors affecting the recovery capability. This research contributes to a deeper understanding of how sustained hypoxic perturbations on respiratory rhythms, as well as the intrinsic mechanisms underlying the external factors and physiological conditions on rhythm recovery.