The generation of respiratory rhythm originates from a population of Pre-Botzinger Complexs, and many kinds of respiratory neurons including the Pre-Botzinger neuron have been suggested to participate in this process, and meanwhile, these respiratory neurons together with the lung constitute a dynamic respiratory network through synaptic connections. The network mechanisms responsible for the generation and variation of respiratory rhythms are still unclear, so this paper explored the issue from the perspective of nonlinear dynamics. By constructing a respiratory network model, whose architecture is very similar to the realistic respiratory anatomic structure, we separately investigated the diverse firing patterns in the single Pre-Botzinger interneuron, and the periodic and synchronous firing activities of the neuronal populations. The obtained model results may provide us some clues in further understanding the mechanisms for the generation of respiratory rhythms.