A multifunctional central pattern generator (CPG) can produce bursting polyrhythms that determine locomotive activity in an animal: for example, swimming and crawling in a leech. Each rhythm corresponds to a specific attractor of the CPG. We employ a Hodgkin-Huxley type model of a bursting leech heart interneuron, and connect three such neurons by fast inhibitory synapses to form a ring. This network motif exhibits multistable co-existing bursting rhythms. The problem of determining rhythmic outcomes is reduced to an analysis of fixed points of Poincare mappings and their attractor basins, in a phase plane defined by the interneurons' phase differences along bursting orbits. Using computer assisted analysis, we examine stability, bifurcations of attractors, and transformations of their basins in the phase plane. These structures determine the global bursting rhythms emitted by the CPG. By varying the coupling synaptic strength, we examine the dynamics and patterns produced by inhibitory networks.
| Identifer | oai:union.ndltd.org:GEORGIA/oai:digitalarchive.gsu.edu:math_theses-1072 |
| Date | 15 July 2009 |
| Creators | Brooks, Matthew Bryan |
| Publisher | Digital Archive @ GSU |
| Source Sets | Georgia State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Mathematics Theses |
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