2009/07/15 by Jonathan Touboul, Touboul, Jonathan, Olivier Faugeras +1
Computer Science · Neuroscience · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Neural Networks Stability and Synchronization #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.0907.2718
openalex publication_date 2009/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Temporal lobe epilepsy is one of the most common chronic neurological disorder characterized by the occurrence of spontaneous recurrent seizures which can be observed at the level of populations through electroencephalogram (EEG) recordings. This paper summarizes some preliminary works aimed to understand from a theoretical viewpoint the occurrence of this type of seizures and the origin of the oscillatory activity in some classical cortical column models. We relate these rhythmic activities to the structure of the set of periodic orbits in the models, and therefore to their bifurcations. We will be mainly interested Jansen and Rit model, and study the codimension one, two and a codimension three bifurcations of equilibria and cycles of this model. We can therefore understand the effect of the different biological parameters of the system of the apparition of epileptiform activity and observe the emergence of alpha, delta and theta sleep waves in a certain range of parameter. We then present a very quick study of Wendling and Chauvel's model which takes into account GABA A inhibitory postsynaptic currents.