Abstract :
[en] 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.
Disciplines :
Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others
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