Modeling the modulation of neuronal bursting: a singularity theory approach
Abstract
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-scales 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.
Keywords
Cite
@article{arxiv.1305.7364,
title = {Modeling the modulation of neuronal bursting: a singularity theory approach},
author = {Alessio Franci and Guillaume Drion and Rodolphe Sepulchre},
journal= {arXiv preprint arXiv:1305.7364},
year = {2013}
}