Spatio-temporal canards in neural field equations
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 sp...
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| Format: | Article |
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American Physical Society
2017
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| Online Access: | https://eprints.nottingham.ac.uk/41292/ |
| _version_ | 1848796241302913024 |
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| author | Avitabile, Daniele Desroches, Mathieu Knobloch, E. |
| author_facet | Avitabile, Daniele Desroches, Mathieu Knobloch, E. |
| author_sort | Avitabile, Daniele |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T19:44:51Z |
| format | Article |
| id | nottingham-41292 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:44:51Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-412922020-05-04T18:41:28Z https://eprints.nottingham.ac.uk/41292/ Spatio-temporal canards in neural field equations Avitabile, Daniele Desroches, Mathieu Knobloch, E. 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. American Physical Society 2017-04-12 Article PeerReviewed Avitabile, Daniele, Desroches, Mathieu and Knobloch, E. (2017) Spatio-temporal canards in neural field equations. Physical Review E, 95 (4). 042205-1. ISSN 1550-2376 https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.042205 doi:10.1103/PhysRevE.95.042205 doi:10.1103/PhysRevE.95.042205 |
| spellingShingle | Avitabile, Daniele Desroches, Mathieu Knobloch, E. Spatio-temporal canards in neural field equations |
| title | Spatio-temporal canards in neural field equations |
| title_full | Spatio-temporal canards in neural field equations |
| title_fullStr | Spatio-temporal canards in neural field equations |
| title_full_unstemmed | Spatio-temporal canards in neural field equations |
| title_short | Spatio-temporal canards in neural field equations |
| title_sort | spatio-temporal canards in neural field equations |
| url | https://eprints.nottingham.ac.uk/41292/ https://eprints.nottingham.ac.uk/41292/ https://eprints.nottingham.ac.uk/41292/ |