The Neurodynamics of Bursting Oscillations in the Hindmarsh-rose Model
Open Access
Author:
Tuznik, Stanley Leonard
Area of Honors:
Mathematics (Behrend)
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Antonio Mastroberardino, Thesis Supervisor Joseph Peter Previte, Thesis Honors Advisor
Keywords:
neurodynamics neuron bursting neuroscience mathematics applied mathematics dynamical systems hindmarsh rose dynamics nonlinear
Abstract:
The Hindmarsh-Rose model is a popular choice for simulating the behavior of a single neuron
as it is able to capture, qualitatively, the spiking and bursting behaviors that are observed exper-
imentally. This three-dimensional nonlinear system relies on a slow adaptation variable which
dynamically switches the neuron from a period of firing to a quiescent period, a phenomenon
known as bursting. We describe the underlying mechanism behind this bursting by reducing the model to a single-parameter system in the phase plane.
