Carleman Embedding Technique: Qualitative Models of Neural Activity

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 project, it is shown that the Carleman Embedding Technique can be applied to both the Fitzhugh Nagumo model and to Van der Pol 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.