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| The pre-Botzinger complex of the mammalian brain stem has been discovered to play a crucial role in generating respiratory rhythms. Excitatory neurons within the pre-Botzinger complex can exhibit different bursting patterns. In this paper, we study different bursting patterns of a self-coupled single cell network of Butera model based on first recurrence map. By the first recurrence map the original model will be reduced to a one-dimensional map. With the sodium conductance changed, the bursting pattern switch from one to another, and the properties of the one-dimensional map are studied. Through the analysis of the map, some analytical conditions for bursting patterns transition from one type to another are confirmed, and numerical results are also presented. |
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