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Temporal lobe epilepsy is one of the most common chronic neurologicaldisorder characterized by the occurrence of spontaneous recurrent seizureswhich can be observed at the level of populations through electroencephalogram(EEG) recordings. This paper summarizes some preliminary works aimed tounderstand from a theoretical viewpoint the occurrence of this type of seizuresand the origin of the oscillatory activity in some classical cortical columnmodels. We relate these rhythmic activities to the structure of the set ofperiodic orbits in the models, and therefore to their bifurcations. We will bemainly interested Jansen and Rit model, and study the codimension one, two anda codimension three bifurcations of equilibria and cycles of this model. We cantherefore understand the effect of the different biological parameters of thesystem of the apparition of epileptiform activity and observe the emergence ofalpha, delta and theta sleep waves in a certain range of parameter. We thenpresent a very quick study of Wendling and Chauvel's model which takes intoaccount GABA A inhibitory postsynaptic currents.

Codimension Two Bifurcations and Rythms in Neural Mass Models