title: Key bifurcations of bursting polyrhythms in 3-cell central pattern generators.
abstract: We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multifunctional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincaré return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the qualitative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic patterns generated by various CPGs in the context of motor control such as gait-switching in locomotion. Our analysis does not require knowledge of the equations modeling the system and provides a powerful qualitative approach to studying detailed models of rhythmic behavior. Thus, our approach is applicable to a wide range of biological phenomena beyond motor control.
authors.affiliation: Applied Technology Associates, Albuquerque, New Mexico, United States of America.
authors.forename: Jeremy
authors.initials: J
authors.lastname: Wojcik
authors.affiliation: Neuroscience Institute, Georgia State University, Atlanta, Georgia, United States of America.
authors.forename: Justus
authors.initials: J
authors.lastname: Schwabedal
authors.affiliation: Neuroscience Institute, Georgia State University, Atlanta, Georgia, United States of America; Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia, United States of America.
authors.forename: Robert
authors.initials: R
authors.lastname: Clewley
authors.affiliation: Neuroscience Institute, Georgia State University, Atlanta, Georgia, United States of America; Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia, United States of America; Department of Computational Mathematics and Cybernetics, Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia.
authors.forename: Andrey L
authors.initials: AL
authors.lastname: Shilnikov
mesh_terms: D063226:Central Pattern Generators / Q000502:physiology*; D005684:Gait / Q000502:physiology; D017629:Gap Junctions / Q000502:physiology; D008124:Locomotion / Q000502:physiology; D008954:Models, Biological; D009046:Motor Neurons / Q000502:physiology*; D010507:Periodicity; D013569:Synapses / Q000502:physiology*
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