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The regulatory mechanism of the respiratory system is always a hot topic in the neurobiology field. Many researchers proposed multitudinous respiratory network models and explored their internal connections. For further understanding the effect of the respiratory system in breathing, we have built a simplified respiratory network model and studied the relations between each neuron in this network. We, firstly, removed the pre-I neuron from the network and found that there are abundant bifurcation

phenomena with respect for the interspike intervals (ISIs). In addition, a large number of unusual firing patterns were observed in the network under conditions of AC stimulation. After adjusting the potassium conductance in the pre-I neuron by a different tonic drive from the d input, we show the transition from bursting patterns to analogous single spiking and, subsequently, convert-bursting patterns. Moreover, when sodium ion channels were removed or synaptic connections and tonic drives in the network were excluded, the network activity showed relevant variations. This may help to explain some functions of ion channels or certain neurons of the network. Finally, the biparametric screening plane with the excitatory synaptic conductance and persistent sodium conductance has been drawn. Graduations in this plane reflected different firing patterns, such as tonic spiking, bursting, and aperiodic bursting. Our results provide important insights for understanding the regulatory mechanisms of the respiratory network and the surrounding structures.