Alan Lloyd Hodgkin and Andrew Huxlley's pioneering work in the early 1950s revolutionized the fields of biophysics and neuroscience. Earning them a Nobel Prize in Medicine Physiology in 1963, their Hodgkin-Huxley (H-H) model was the first model offering an apt mathematical and quantitative description of neural action potential propagation. Its physiological relevance notwithstanding, what stands as the arguably most profound result of their work is the unveiling of the innate dynamical nature of neurons. Since then, numerous efforts have gone into simplifying the H-H model and creating novel dynamical models of neural firing. One of the most prominent of such models is the 2D FitzHugh-Nagumo (FHN) model. Given its simplicity, the FHN model fails to simulate a rich set of neural firing behaviour. This thesis aims to extend on the FHN model by using it as a basis for a 3D model capable of simulating a richer set of neural behaviours. To that end, tools of dynamical systems analysis, —such as linear stability and bifurcation analysis— are used to study the dynamical workings of the 3D model, and how they pertain to the different neural behaviours exhibited.
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