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Normal form analysis of a mean-field inhibitory neuron model

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Normal form analysis of a mean-field inhibitory neuron model

Tsakanikas, Loukia (2012) Normal form analysis of a mean-field inhibitory neuron model. Masters thesis, Concordia University.

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Abstract

In neuroscience one of the open problems is the creation of the alpha rhythm detected
by the electroencephalogram (EEG). One hypothesis is that the alpha rhythm
is created by the inhibitory neurons only. The mesoscopic approach to understand
the brain is the most appropriate to mathematically modelize the EEG records of the
human scalp. In this thesis we use a local, mean-field potential model restricted to
the inhibitory neuron population only to reproduce the alpha rhythm. We perform
extensive bifurcation analysis of the system using AUTO.We use Kuznetsov’s method
that combines the center manifold reduction and normal form theory to analytically
compute the normal form coefficients of the model. The bifurcation diagram is largely
organised around a codimension 3 degenerate Bogdanov-Takens point. Alpha rhythm
oscillations are detected as periodic solutions.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Tsakanikas, Loukia
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:April 2012
Thesis Supervisor(s):van Veen, Lennaert and Doedel, Eusebius
ID Code:974722
Deposited By:LOUKIA TSAKANIKAS
Deposited On:30 Oct 2012 14:55
Last Modified:30 Oct 2012 14:55
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