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
Special Session 112: Nonlinear dynamics in neuroscience
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.