Spatio-temporal canards in neural field equations

Avitabile, Daniele and Desroches, Mathieu and Knobloch, E. (2017) Spatio-temporal canards in neural field equations. Physical Review E, 95 (4). 042205-1. ISSN 1550-2376

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Abstract

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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1103/PhysRevE.95.042205
Depositing User: Eprints, Support
Date Deposited: 14 Mar 2017 09:44
Last Modified: 19 Apr 2017 08:06
URI: http://eprints.nottingham.ac.uk/id/eprint/41292

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