The three-phase respiratory pattern observed during normal breathing changes with alterations in metabolic or physiological conditions. A recent study using in situ perfused rat brain preparations demonstrated a reorganization of the respiratory pattern with sequential reduction of the brain stem respiratory network. Specifically, with removal of the pons, the normal three-phase pattern transformed to a two-phase inspiratory-expiratory pattern, and, with more caudal transections, to one-phase, intrinsically generated inspiratory oscillations (Smith et al. 2007). A minimal neural network proposed to reproduce these transformations includes (1) a ring-like mutually inhibitory network composed of the post-inspiratory, augmenting expiratory, and early-inspiratory neurons, and (2) an excitatory pre-inspiratory neuron, with persistent sodium current (INaP)-dependent intrinsic bursting properties, that dynamically participates in the expiratory-inspiratory phase transition and inspiratory phase generation. We used activity-based single neuron models and applied numerical simulations, bifurcation methods, and fast-slow decomposition to describe the behavior of this network in the functional states corresponding to the three-, two-, and one-phase oscillatory regimes, as well as to analyze the transitions between states and between respiratory phases within each state. We demonstrate that, although INaP is not necessary for the generation of three- and two-phase oscillations, it contributes to control of oscillation period in each state. We also show that the transitions between states can be produced by progressive changes of drives to particular neurons and proceed through intermediate regimes, featuring high-amplitude late-expiratory and biphasic-expiratory activities or ectopic burst generation. Our results provide important insights for understanding the state dependent mechanisms for respiratory rhythm generation and control.