We perform visualization of the nullcline dynamics around threshold, and characterize important geometric properties via dominant scale analysis, which avoids the need to make asymptotic approximations. In particular, we analyze the transient dynamics during the passage through the ghost of a saddle-node bifurcation in the (V, m) phase-plane projection of a local 3D approximation to the 4D H-H equations (where sodium inactivation h is held constant).
Clewley and Chung: Geometric analysis of soft thresholds in action potential initiation and the consequences for understanding phase response curves and model tuning. BMC Neuroscience 2012 13(Suppl 1):P165. doi: 10.1186/1471-2202-13-S1-P165
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