So, the program nears completion, however, I anticipated that it would be done by today at the latest. There are still some bugs to fix. First, it is not robust doing the step size... it claims I'm trying to make a matrix of non-integer values (which I'm not). I think it's the program, since it works with only some step sizes, but not all. Another problem, which is an integral part of the program, is getting it to graph in two colors. We can then infer the location of the bifurcation line as the region where the points change color.

Fortunately, the program as is should be easy to convert to the 3-D case, which should be interesting (I don't know how I'd graph that, but then again, I have some time to think about it). I'm only worried that MatLab will be just finicky with the program and not want to do it.

I'm going to see if I can resolve these problems tonight, then I'll do some more background research and applications. By the way, here's an interesting link about its applications.

It doesn't explicitly talk about how it applies, but it gives the gist of what's going on during this natural process. The nonlinear equation comes into play here...

Well, that's it for now; I better get cracking at this thing if I want it to be handle equations like that one above for any case...

## 09 June 2008

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