Add SNIC line to phase plane

[hinsley]

Currently, my understanding is that the SNIC line is computed by fixing parameters and the x and Ca variables and computing the average voltage value over a trajectory for every point in the Ca-x plane, then extracting a high-low contour from the resulting average voltage surface. This is fairly costly; I suspect there is a way to compute this curve through other means. If so, it could be integrated into the interactive explorer.

[dbloom2]

While it would be nice for the interactive explorer, intention here was for the sweep plots and animations.

I would suggest splitting the interactive explorer as a separate issue.

If we want to incorporate into the interactive explorer, I do believe there are a few alternatives that may be computationally more efficient, but may sacrifice accuracy. For example, we could pre-calculate a representative sample from sweep, or another option might be to use level curves.

[hinsley]

I did some computations by hand and came to the conclusion that the SNIC line likely has little (or nothing) to do with the $\Delta{\textrm{Ca}}$ and $\Delta{\textrm{x}}$ parameters. Looking over the paper detailing the model, Jack's Figure 5 appears to reinforce this suspicion: Only the $\Delta_{\textrm{x}}$ has any effect on the right-hand side of the SNIC curve, and it is relatively minimal.

[hinsley]

Just wanted to note here that it's possible the SNIC curve might be obtained by taking the submanifold of the $x$ nullcline dune given by the $V=0$ level set of the $x$ nullclines -- this needs some further investigation before saying it's certainly true though.