Birdsong emerges when a set of highly interconnected brain areas manage to generate a complex output. The similarities between birdsong production and human speech have positioned songbirds as unique animal models for studying learning and production of this complex motor skill. In this work, we developed a low dimensional model for a neural network in which the variables were the average activities of different neural populations within the nuclei of the song system. This neural network is active during production, perception and learning of birdsong. We performed electrophysiological experiments to record neural activity from one of these nuclei and found that the low dimensional model could reproduce the neural dynamics observed during the experiments. Also, this model could reproduce the respiratory motor patterns used to generate song. We showed that sparse activity in one of the neural nuclei could drive a more complex activity downstream in the neural network. This interdisciplinary work shows how low dimensional neural models can be a valuable tool for studying the emergence of complex motor tasks