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The respiratory Central Pattern Generator (rCPG) is a neural circuit located in the brainstem, generating the physiological rhythmic breathing pattern of alternating inspiration and expiration. In this work, we propose a mathematical model of the rCPG which incorporates physiological feedback mechanisms. Numerical simulations of a closed-loop model of the rCPG with a lung and gas exchange model confirm the ability of the proposed model to reproduce the behavior of the rCPG in several important physiological regimes.