Help Interpreting These Scatter Plots

I've calibrated multiple times a model with three parameters: $a$, $b$ and $c$. I graphed each pair of resulting parameters to get an idea of the correlations and got these very strange plots:

Here is a 3D plot:

I'd appreciate some thoughts on how to interpret these. Obviously there seems to be some extreme dependence, but are these results characteristic of anything? What conclusions can we draw from these?

• Can you say more about what you're doing? Oct 22, 2015 at 23:07

The most striking feature seems to be that nonzero $a$ and nonzero $b$ seem to be mutually exclusive - that is, if $a$ is nonzero, $b$ must be 0 and vice versa. I can't think of a good example of this in the real world. It's not just an inverse relationship; it's an exclusionary one.