This website presents my project thesis, in support of the degree of Master of Engineering Mathematics (MEng). 

This project concerns the study of a mathematical model of bursting in the electrical activity of excitable brain cells. These cells can be stimulated to induce electrical periodic bursting activity, an activity that is vital for the cellular physiological functions within and between cells. There is a great demand to understand the excitable behaviour of such cells in order to repair the damage or any undesirable effect caused by the dysfunctional excitable cells of the living system.

Apart from the qualitative approach of bifurcation analysis to study the cell model, we demonstrate how the geometrical structure of a smooth surface, formed by a family of one-dimensional stable manifolds, organise the dynamics of the system and acts as a mechanism that affects the termination of the bursting phase. It is also our aim to explore the mechanism of resetting the phase or rhythm of excitable cells, using the so-called method of phase-resetting, with the hope that it may contribute for a better understanding on the mechanism of excitability in excitable cells.

To navigate this site please select from the list of contents to the left or the navigation bars below every page. The full report (in pdf) can be downloaded here.