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Modeling the modulation of neuronal bursting: A singularity theory approach

Franci, A and Drion, G and Sepulchre, R (2014) Modeling the modulation of neuronal bursting: A singularity theory approach. SIAM Journal on Applied Dynamical Systems, 13. pp. 798-829.

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Abstract

© 2014 Society for Industrial and Applied Mathematics. Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting modulation. The proposed approach combines singularity theory and geometric singular perturbations to capture the geometry of multiple time-scale attractors in the neighborhood of high-codimension singularities. We detect a three-time-scale bursting attractor in the universal unfolding of the winged cusp singularity and discuss the physiological relevance of the bifurcation and unfolding parameters in determining a physiological modulation of bursting. The results suggest generality and simplicity in the organizing role of the winged cusp singularity for the global dynamics of conductance-based models.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:38
Last Modified: 09 Nov 2017 01:28
DOI: