Spatiotemporal canards in neural field equations
- Others:
- School of Mathematical Sciences [Nottingham] ; University of Nottingham, UK (UON)
- Mathématiques pour les Neurosciences (MATHNEURO) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
- COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)
- Department of Physics [Berkeley] ; University of California [Berkeley] (UC Berkeley) ; University of California (UC)-University of California (UC)
Description
Canards are special solutions to ordinary differential equations that follow invariant repelling slow manifolds for long time intervals. In realistic biophysical single-cell models, canards are responsible for several complex neural rhythms observed experimentally, but their existence and role in spatially extended systems is largely unexplored. We identify and describe a type of coherent structure in which a spatial pattern displays temporal canard behavior. Using interfacial dynamics and geometric singular perturbation theory, we classify spatiotemporal canards and give conditions for the existence of folded-saddle and folded-node canards. We find that spatiotemporal canards are robust to changes in the synaptic connectivity and firing rate. The theory correctly predicts the existence of spatiotemporal canards with octahedral symmetry in a neural field model posed on the unit sphere.
Abstract
International audience
Additional details
- URL
- https://hal.inria.fr/hal-01558887
- URN
- urn:oai:HAL:hal-01558887v1
- Origin repository
- UNICA