Final answer:
The respiratory rate during REM sleep is irregular and influenced by the respiratory center in the brain.
Step-by-step explanation:
The respiratory rate during rapid eye movement (REM) sleep, which is a period of sleep characterized by brain waves very similar to those during wakefulness with darting movements of the eyes under closed eyelids, tends to be irregular. This irregularity in breathing during REM sleep contrasts with the regular, rhythmic patterns observed during non-REM sleep. The respiratory rate during REM sleep can fluctuate and is influenced by the respiratory center within the medulla oblongata in the brain, which responds to changes in carbon dioxide, oxygen, and pH levels in the blood.