Qualitative Models of Neural Activity and the Carleman Embedding Technique.

<p>The two variable Fitzhugh Nagumo model behaves qualitatively like the four variable Hodgkin-Huxley space clamped system and is more mathematically tractable than the Hodgkin Huxley model, thus allowing the action potential and other properties of the Hodgkin Huxley system to be more readily be visualized. In this thesis, it is shown that the Carleman Embedding Technique can be applied to both the Fitzhugh Nagumo model and to Van der Pol's model of nonlinear oscillation, which are both finite nonlinear systems of differential equations. The Carleman technique can thus be used to obtain approximate solutions of the Fitzhugh Nagumo model and to study neural activity such as excitability.</p>

Name thesis:degree_name

MS (Master of Science)

Level thesis:degree_level

Thesis - unrestricted

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.issued

2009

Author dc:creator

• Gezahagne, Azamed Yehuala

• Excitability
• Green's function
• Carleman embedding
• Fitzhugh Nagumo
• Applied Mathematics
• Non-linear Dynamics
• Physical Sciences and Mathematics

Statement dc:rights

• Copyright by the authors.

Repository record dc:identifier

https://dc.etsu.edu/etd/1875

OAI identifier oai:identifier

oai:dc.etsu.edu:etd-3227