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Full-Text Articles in Physical Sciences and Mathematics
A Variation Of The Carleman Embedding Method For Second Order Systems., Charles Nunya Dzacka
A Variation Of The Carleman Embedding Method For Second Order Systems., Charles Nunya Dzacka
Electronic Theses and Dissertations
The Carleman Embedding is a method that allows us to embed a finite dimensional system of nonlinear differential equations into a system of infinite dimensional linear differential equations. This technique works well when dealing with first-order nonlinear differential equations. However, for higher order nonlinear ordinary differential equations, it is difficult to use the Carleman Embedding method. This project will examine the Carleman Embedding and a variation of the method which is very convenient in applying to second order systems of nonlinear equations.
Qualitative Models Of Neural Activity And The Carleman Embedding Technique., Azamed Yehuala Gezahagne
Qualitative Models Of Neural Activity And The Carleman Embedding Technique., Azamed Yehuala Gezahagne
Electronic Theses and Dissertations
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 …