Spatiotemporal canards in neural field equations

Physical Review. E
D AvitabileE 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.

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Citations

Jan 20, 2018·Physical Review. E·Jose M Esnaola-AcebesErnest Montbrió
Dec 12, 2017·Proceedings. Mathematical, Physical, and Engineering Sciences·D AvitabileM Krupa
Jul 18, 2019·Bulletin of Mathematical Biology·Anton ChizhovSerafim Rodrigues
Mar 17, 2018·Journal of Computational Neuroscience·Nikhil KrishnanZachary P Kilpatrick

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