1School of Mathematical Sciences, University of Nottingham, Nottingham, UK
A piece-wise linear model of the Fitz Hugh-Nagumo model that supports a Canard solution will be presented. Periodic orbits (both small and large amplitude) are obtained in closed form; For globally gap junctions coupled networks we show further how to study network solutions describing synchronous states. Importantly we will be able to analyse stability in the strong coupling regime. We need this analysis to explore the existence of Mixed Mode Oscillations and their dependence on system parameters; At the end, the importance of such Mixed Mode Oscillations in generating brain rhythms will be discussed.