Animation by Timothy Jones based on the journal article "Reduction of a model of an excitable cell to a one-dimensional map" (Physica D 202 (2005) 37-59) by Dr. Georgi S. Medvedev. Here we see the 'fast subsystem' of the Chay model animated through the parameter u from -0.23 to +0.23. We see an Andronov-Hopf bifurcation followed by a Saddle-node bifurcation (when the nullclines further intersect) and ending with a Homoclinic bifurcation (when the AH associated cycle merges with one of the SN fixed points). Dr. Medvedev writes: "The sharpness of the transition is due to the fact that the fast subsystem is a singularly perturbed system of ODEs. This is called canard transition."

The Matlab code for this model can be found here and the linux shell script used to cycle through for animation purposes can be found here. A similar Maple worksheet is available. This video is also on YouTube (click on the high-quality option below the video, though).

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