Abstract
The pre-Bötzinger complex of the mammalian brain stem plays a crucial role in the respiratory rhythms generation. Neurons within the pre-Bötzinger complex have been found experimentally to yield different firing activities. In this paper, we study the spiking and bursting activities related to the respiratory rhythms in the pre-Bötzinger complex based on a mathematical model proposed by Butera. Using the one-dimensional first recurrence map induced by dynamics, we investigate the different bursting patterns and their transition of the pre-Bötzinger complex neurons based on the Butera model, after we derived a one-dimensional map from the dynamical characters of the differential equations, and we obtained conditions for the transition of different bursting patterns. These analytical results were verified through numerical simulations. We conclude that the one-dimensional map contains similar rhythmic patterns as the Butera model and can be used as a simpler modeling tool to study fast–slow models like pre-Bötzinger complex neural circuit.
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