In Fig. 1 you show that parabolic bursting is produced when you modify the parameter values. It would be helpful to explain why these modified parameter values are not used as the default parameter values.
GdeV: Interestingly, the early papers do not show any bursting with a parabolic profile. I've added a note in the figure caption and the main text to clarify that the default parameter values used are those specified in the Plant (1981) paper.
I appreciated the historical overview of how this looked to Plant - like many theorists my knowledge of the model comes mainly from analyses by others, such as Rinzel, that came later.
My only suggestion is to provide some commentary, or at least links, to more recent work updating the biophysical modeling of R15, which also continued to progress along with the analysis. My impression is that the mechanism of bursting was never definitively settled (and when has it ever been settled for any bursting model?), but the participants in the debate moved on to other things. Two who did some further work were Rob Butera and Carmen Canavier. A few representative citations (or ask Rob or Carmen):
Butera RJ. Multirhythmic bursting. Chaos. 1998 Mar;8(1):274-284.
Butera RJ Jr, Clark JW Jr, Byrne JH. Dissection and reduction of a modeled bursting neuron. J Comput Neurosci. 1996 Sep;3(3):199-223.
Butera RJ Jr, Clark JW Jr, Canavier CC, Baxter DA, Byrne JH. Analysis of the effects of modulatory agents on a modeled bursting neuron: dynamic interactions between voltage and calcium dependent systems. J Comput Neurosci. 1995 Mar;2(1):19-44. Erratum in: J Comput Neurosci 1996 Sep;3(3):265.
Canavier CC, Baxter DA, Clark JW, Byrne JH. Multiple modes of activity in a model neuron suggest a novel mechanism for the effects of neuromodulators. J Neurophysiol. 1994 Aug;72(2):872-82.