Network torus canards and their mean-field limits

Emre Baspinar (1, 2, 3) , Daniele Avitabile (4) , Mathieu Desroches (3)

1 NeuroPSI - Institut des Neurosciences Paris-Saclay
2 CNRS - Centre National de la Recherche Scientifique
3 MATHNEURO - Mathématiques pour les Neurosciences
4 VU - Vrije Universiteit Amsterdam [Amsterdam]

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.

Domaines: Neurosciences; Systèmes dynamiques [math.DS]

Emre Baspinar, Daniele Avitabile, Mathieu Desroches. Network torus canards and their mean-field limits. 2022. ⟨hal-03588795⟩