Compact bifurcation analysis of the Epileptor

Abstract

The Epileptor is a phenomenological model able to reproduce the activity of the most common class, in terms of dynamics, of epileptic seizures, characterized by having square-wave bursting properties. It also encodes an additional mechanism to account for interictal spikes and spike and wave discharges. This model is being used in large-scale brain modeling of epileptic patients with the goal of improving surgical outcomes. Here we use insights from a more generic model for square-wave bursting, based on the Unfolding Theory approach, to guide the bifurcation analysis of the Epileptor. This allows to understand how the Epileptors parameters can be modified to produce activities for other seizures classes (i.e. other onset/offset bifurcation pairs) as observed in patients and to unveil how the interaction with the additional mechanism for spike and wave discharges alters the bifurcation structure of the main burster.