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Spatio-temporal canards in neural field equations

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

Authors

Daniele Avitabile Daniele.Avitabile@nottingham.ac.uk

Mathieu Desroches mathieu.desroches@inria.fr

E. Knobloch



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.

Journal Article Type Article
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 1550-2376
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 95
Issue 4
APA6 Citation Avitabile, D., Desroches, M., & Knobloch, E. (in press). Spatio-temporal canards in neural field equations. Physical Review E, 95(4), doi:10.1103/PhysRevE.95.042205
DOI https://doi.org/10.1103/PhysRevE.95.042205
Publisher URL https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.042205
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf


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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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