Introduction Sleep apnea/hypopnea syndrome (SAHS) can change brain structure and function. These alterations are related to respiratory event-induced abnormal sleep, however, how brain activity changes during these events is less well understood. Methods To study information content and interaction among various cortical regions, we analyzed the variations of permutation entropy (PeEn) and symbolic transfer entropy (STE) of electroencephalography (EEG) activity during respiratory events. In this study, 57 patients with moderate SAHS were enrolled, including 2804 respiratory events. The events terminated with cortical arousal were independently researched. Results PeEn and STE were lower during apnea/hypopnea, and most of the brain interaction was higher after apnea/hypopnea termination than that before apnea in N2 stage. As indicated by STE, the respiratory events also affected the stability of information transmission mode. In N1, N2, and rapid eye movement (REM) stages, the information flow direction was posterior-to-anterior, but the anterior-to-posterior increased relatively during apnea/hypopnea. The above EEG activity trends maintained in events with cortical arousal. Conclusions These results may be related to the intermittent hypoxia during apnea and the cortical response. Furthermore, increased frontal information outflow, which was related to the compensatory activation of frontal neurons, may associate with cognitive function.