Videoconference: Slow-fast analysis of neural bursters: old and new скачать в хорошем качестве

Videoconference: Slow-fast analysis of neural bursters: old and new

Slow-fast analysis of neural bursters: old and new Mathieu Desroches, Inria, Sophia Antipolis (Méditerranée Research Centre) May 22nd 2020 / 22 mai 2020 (Séminaire CAMBAM Seminar Series) http://www.crm.umontreal.ca/labo/camb... Organizers / Organisateurs: Anmar Khadra In this talk, I will present recent work on multiple-timescale dynamical systems displaying complex oscillations with both slow and fast components. After a brief review of bursting oscillations and the role of so-called spike-adding transitions in square-wave bursters, I will introduce a four-dimensional extension of this scenario which creates small-amplitude slow (sub-threshold) oscillations in between bursts, mediated by so-called canard solutions. In the second half of the talk, I will revisit another type of four-dimensional bursting scenario with two slow variables, namely parabolic bursting, and provide explanations on how the spike-adding mechanism in such bursters is also organised by canards but of a different type than before. This will be showcased on several examples of parabolic bursters, both biophysical ones like the Plant model, and simplified ones like theta models. Finally, I will show how the burst-excitable structure of networks of theta model may persist across scales up to some mean-field limit. [This is based on joint papers with D Avitabile (Amsterdam), GB Ermentrout (Pittsburgh), TJ Kaper (Boston), M Krupa (Nice) and S Rodrigues (Bilbao)]