| We demonstrate a motif of three reciprocally inhibitory cells that is able to produce multiple patterns of bursting rhythms. Through the examination of the qualitative geometric structure of two-dimensional maps for phase lag between the cells we reveal the organizing centers of emergent polyrhythmic patterns and their bifurcations, as the asymmetry of the synaptic coupling is varied. The presence of multistability and the types of attractors in the network are shown to be determined by the duty cycle of bursting. This analysis does not require knowledge of the equations that model the system, and so provides a powerful new approach to studying regulatory networks. Thus, the approach is applicable to a variety of biological phenomena beyond motor control. |
