The pre-Bötzinger complex is a crucial region for the generation of respiratory rhythms in mammals. Peripheral chemoreceptors have a significant impact on respiratory rhythm by monitoring changes in blood oxygen and carbon dioxide concentrations. This study introduces a closed-loop respiratory control model that is driven by electromagnetic induction and is based on the activation of pre-Bötzinger complex neurons. The model incorporates various factors including the motor pool, lung volume, lung oxygen, blood oxygen, and chemoreceptors. The response of the system imposed the same hypoxic perturbation is investigated under different electromagnetic induction, and the control effect of the magnetic flux feedback coefficient on the recovery of mixed rhythms is examined. Using bifurcation analysis and numerical simulations, it has been found that the magnetic flux feedback coefficient has a significant impact on the recovery ability of respiratory rhythm. The dynamic mechanism of the magnetic flux feedback coefficient on different hypoxic responses in closed-loop systems are revealed. Dynamics analysis indicates that under certain electromagnetic induction, the mixed bursting rhythm in the closed-loop system can autoresuscitate if the bifurcation structure before and after applying hypoxia perturbation are completely identical. However, when the bifurcation structure before and after applying hypoxia perturbation are different, the mixed bursting rhythm in the system cannot autoresuscitate. In addition, for cases where automatic recovery is not achieved under mild electromagnetic induction, increasing the magnetic flux feedback coefficient appropriately can lead to autoresuscitate of the system, which is closely related to the Hopf bifurcation and fold bifurcation of limit cycle. This study will help to understand the impact of the interaction between the central respiratory and peripheral chemoreceptive feedback on respiratory rhythm, as well as the control role of external induction on the hypoxic response.