Spatio-temporal canards in neural field equations

Avitabile, Daniele; Desroches, Mathieu; Knobloch, E.

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.

Citation

Avitabile, D., Desroches, M., & Knobloch, E. (in press). Spatio-temporal canards in neural field equations. Physical Review E, 95(4), https://doi.org/10.1103/PhysRevE.95.042205

• Journal Article Type: Article
• Acceptance Date: Mar 10, 2017
• Online Publication Date: Apr 12, 2017
• Deposit Date: Mar 14, 2017
• Publicly Available Date: Apr 12, 2017
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 1550-2376
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 95
• Issue: 4
• DOI: https://doi.org/10.1103/PhysRevE.95.042205
• Public URL: https://nottingham-repository.worktribe.com/output/855387
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.042205