Display Abstract
 Title Periodic solutions of the FitzHugh-Nagumo equations - a computer assisted proof
 Name Aleksander Czechowski Country Poland Email czechows@ii.uj.edu.pl Co-Author(s) Piotr Zgliczy\'nski Submit Time 2014-02-27 07:59:57 Session Special Session 112: Nonlinear dynamics in neuroscience
 Contents In this talk I will consider the FitzHugh-Nagumo slow-fast system arising from the travelling wave equation for the FitzHugh-Nagumo neuron model with diffusion. The existence of periodic solutions of this system is well known for timescales ratio parameter $\varepsilon \in (0, \varepsilon_{0}]$, $\varepsilon_{0}$ sufficiently small. The method I will present allows proving the existence of such solutions for $\varepsilon_{0}$ explicit, by combining rigorous numerical integration with the use of topological methods.