Phase-lag return mappings for a 3 cell multifunctional central pattern generator
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KeywordsDuty Cycle Return Mapping Detailed Model External Input Rhythmic Activity
We describe and expand on a novel computational approach to reduce detailed models of central pattern generation to equationless return mapping for the phase lags between the constituting bursting interneurons .
Such mappings are then studied geometrically as the model parameters, including coupling properties of inhibitory and excitatory synapses, or external inputs are varied. Bifurcations of the fixed points and invariant circles of the mappings corresponding to various types of rhythmic activity are examined. These changes uncover possible biophysical mechanisms for control and modulation of motor-pattern generation. 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 thank W. Kristan, A. Neiman, P. Ashwin, C. Laing, and R. Lin for valuable suggestions.We acknowledge support from NSF Grants CISE/CCF-0829742 (to R.C.), DMS-1009591, RFFI Grant No. 08-01-00083 (to A.S.) and “Grant opportunities for Russian scientists living abroad” Project No. 14.740.11.0919, and the GSU Brains & Behavior program.
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