Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 238, Issue 16, Pages 1598-1614Publisher
ELSEVIER
DOI: 10.1016/j.physd.2009.04.017
Keywords
Stellate cell; Canard; Folded node; Mixed-mode oscillation; Relaxation oscillation
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Funding
- University of Sydney Bridging Support Grant
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Experimental recordings of the membrane potential of stellate cells within the entorhinal cortex show a transition from Subthreshold oscillations (STOs) via mixed-mode oscillations (MMOs) to relaxation oscillations under increased injection of depolarizing current. Acker et al. introduced a 7D conductance based model which reproduces many features of the oscillatory patterns observed in these experiments. For the first time, we present a comprehensive bifurcation analysis of this model by using the software package AUTO. In particular, we calculate the stable MMO branches within the bifurcation diagram of this model, as well as other MMO patterns which are unstable. We then use geometric singular perturbation theory to demonstrate how the bifurcations are governed by a 3D reduced model introduced by Rotstein et al. We extend their analysis to explain all observed MMO patterns within the bifurcation diagram. A key role in this bifurcation analysis is played by a novel homoclinic bifurcation structure connecting to a saddle equilibrium on the unstable branch of the corresponding critical manifold. This type of homoclinic connection is possible due to canards of folded node (folded saddle-node) type. (C) 2009 Elsevier B.V. All rights reserved.
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