Type of Document Master's Thesis Author Malashchenko, Tatiana Igorevna URN etd-07312007-195922 Title A MECHANISM OF CO-EXISTENCE OF BURSTING AND SILENT REGIMES OF ACTIVITIES OF A NEURON Degree Master of Science Department Physics and Astronomy Advisory Committee
Advisor Name Title Andrey Shilnikov Committee Member Donald Edwards Committee Member Gennady Cymbalyuk Committee Member Unil Perera Committee Member Vadym Apalkov Committee Member Keywords
- computational neuroscience
- bifurcation analysis
- multistability
- co-existence
- silence
- Bursting
Date of Defense 2007-07-17 Availability unrestricted Abstract The co-existence of bursting activity and silence is a common property of various neuronal models. We describe a novel mechanism explaining the co-existence of and the transition between these two regimes. It is based on the specific homoclinic and Andronov-Hopf bifurcations of the hyper- and depolarized steady states that determine the co-existence domain in the parameter space of the leech heart interneuron models: canonical and simplified. We found that a sub-critical Andronov-Hopf bifurcation of the hyperpolarized steady state gives rise to small amplitude sub-threshold oscillations terminating through the secondary homoclinic bifurcation. Near the corresponding boundary the system can exhibit long transition from bursting oscillations into silence, as well as the bi-stability where the observed regime is determined by the initial state of the neuron. The mechanism found is shown to be generic for the simplified 4D and the original 14D leech heart interneuron models.Files
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