<p>Respiratory disorders characterized by irregular breathing patterns can be life-threatening. In this study, we investigate the potential of optogenetic interventions as a therapeutic strategy by focusing on the pre-Bötzinger complex (pre-BötC), a critical respiratory control center in the brainstem. We develop a closed-loop mathematical model of the pre-BötC and integrate Channelrhodopsin-2 (ChR2) stimulation, which is modeled as an equivalent ion channel current, to modulate respiratory rhythm. Our results demonstrate that ChR2-mediated activation regulates the transition between different breathing states depending on the laser intensity and stimulation duration. As the intensity increases, the system initially remains in a tachypnea state, then transitions to eupnea, and ultimately returns to tachypnea. Under specific parameter conditions, the model also predicts the emergence of mixed bursting patterns within single respiratory cycles. Additionally, we use bifurcation analysis to explain the mechanisms underlying these transitions. These findings offer theoretical support for the use of optogenetic interventions in controlling respiratory rhythms and provide insights into potential treatments for respiratory disorders.</p>