Back to Departmental Colloquium: Spring 2005
Departmental Colloquium
Date: Thursday, Feb 10, 2005
Time: 4:15PM
Location: JWB 335
Special Colloquium Thursday
Mathematical Analysis of a Neuronal Network: Transitions Between Activity Modes
Title |
Mathematical Analysis of a Neuronal Network: Transitions Between Activity Modes |
Abstract |
A mathematical model of a brain region called the Pre-Botzinger complex consists of a large system of coupled non-linear ODEs. I will present a mathematical analysis of this system that allows to elucidate the multi-dimensional bifurcation structure responsible for transitions between activity modes (quiescence, bursting and spiking). In particular, I will describe a non-standard fast-slow dissection approach, incorporating averaging in the slow subsystem. The results advance the current mathematical understanding of networks of bursting neurons, as well as answer a number of biologically-motivated questions. For example, this analysis clarifies the role of coupling in selecting burst frequency, as well as the mechanisms via which a network can burst synchronously for a much wider range of parameters than in the case of individual cells. |
Mathematical Biology
Data Science and Machine Learning
Applied Mathematics