Network torus canards and their mean-field limits

Creators: Baspinar, Emre; Avitabile, Daniele; Desroches, Mathieu

Others:: Institut des Neurosciences Paris-Saclay (NeuroPSI) ; Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Mathématiques pour les Neurosciences (MATHNEURO) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); Vrije Universiteit Amsterdam [Amsterdam] (VU); European Project: 785907,H2020,HBP SGA2(2018); European Project: 945539,H2020,H2020-SGA-FETFLAG-HBP-2019,HBP SGA3(2020)

Description

We show that during the transition from and to elliptic burstings both classical and mixed-type torus canards appear in a Wilson-Cowan type neuronal network model, as well as in its corresponding mean-field framework. We show numerically the overlap between the network and mean-field dynamics. We comment on that mixed-type torus canards result from the nonsymmetric fast subsystem. This nonsymmetricity provides the dynamics linked to an associated canonical form presented in [7], and it occurs mainly due to the three-timescale nature of the Wilson-Cowan type models.

Network torus canards and their mean-field limits

Description

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