A class of simple networks for modeling spike-wave discharges

Absence epilepsy is a widespread among children and adolescents form of disease, manifestating itself on EEG with spike-wave discharges (SWDs). It was shown, just as a proof of concept, that SWDs can be considered as a long transient process rather than attractor in a phase space. In this work, we investigate this hypothesis in detail, studying a small class of simple mathematical models consisting of 14 identical FitzHugh–Nagumo neurons, organized in accordance with modern concepts of the thalamo-cortical network of the brain. Some models belonging to the class studied demonstrate rather long transient processes in response to a short in time external driving from an individual neuron modeling the trigeminal nerve.