COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics


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Colloquium: Dynamic Behavior of Neuronal Groups Using a Phenomenological Model


4:10 p.m. Neill Hall 5W

Indika Rajapakse

Abstract:The framework for thinking about electrical activities in the brain and describing them using mathematical formulations was introduced about fifty years ago, by Hodgkin and Huxley. Since then mathematical models have played an important role in the study of neuroscience. In recent times, the modeling approach has become a potent research strategy in sleep research due to the use of imaging techniques and the need to quantify new hypotheses. The current thinking on sleep is that it is a property of neuronal groups and that neuronal groups oscillate between sleep and awake states. As part of sleep research, our work involves constructing a phenomenological model that provides the quantitative description of the dynamics of a neuronal group. A neuronal group consists of a large number of highly interconnected neurons. From experiments, it has been shown that neuronal groups can oscillate. Our study determines the conditions that lead the phenomenological model to have a stable oscillation. Furthermore, we discuss some bifurcation properties of two mutually coupled, identical neuronal groups.