The Role of Duty Cycle in a Three Cell Central Pattern Generator

We describe a novel computational approach to reduce detailed models of central pattern generation to an equationless mapping that can be studied geometrically. Changes in model parameters, coupling properties, or external inputs produce qualitative changes in the mapping. These changes uncover possible biophysical mechanisms for control and modulation of rhythmic activity. Our analysis does not require knowledge of the equations that model the system, and so provides a powerful new approach to studying detailed models, applicable to a variety of biological phenomena beyond motor control. We demonstrate our technique on a motif of three reciprocally inhibitory cells that is able to produce multiple patterns of bursting rhythms. In particular, we examine the qualitative geometric structure of two-dimensional maps for phase lag between the cells.