Non-physical Jounce Examples in Nature

What are some good examples of jounce in the non-physics arena?

The reason I ask is that A) it's already difficult for a lay to visualize it in the physical arena and B) you never hear of too many examples past the second derivative outside of said physical arena.

Jerk is relatively easy to perceive when one slams on the breaks and then lets them go, and the best way to describe jounce is an amusement park ride since you're always being jerked around.

Outside of physics, it's a little hard to come by, so I'd like to see if there are other ways of perceiving higher order derivatives in other disciplines.

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What is the question? Money is not the problem. – Ross Millikan Nov 9 '12 at 4:50
Non-physical/engineering/etc examples of 4th+ derivatives. I have an idea of how to apply for finance, but I'm not totally sure, so I'd like to see other examples for comparison. – Joe Coder Guy Nov 9 '12 at 4:53
Aargh. The question could use a lot of improvement, sure, but it's not all that hard to figure out what Joe wants (or at least to make a reasonable guess). I was in the middle of writing an answer when it got closed. Come on, Eric, easy on the moderator superpowers. – Gerry Myerson Nov 9 '12 at 4:55
In determining stability of nonhyperbolic fixed points of one-dimensional discrete dynamical systems, it may be necessary to evaluate the so-called Schwarzian derivative. The formula for the Schwarzian derivative involves the third derivative of the function in question. – Gerry Myerson Nov 9 '12 at 5:10
@GerryMyerson: It looks like Austin Mohr and you have understood OP better than me. Congrats and sorry for voting to close. – Ross Millikan Nov 9 '12 at 5:21
Given differentiable $f:I\to I$ where $I$ is an interval, and $x$ such that $f(x)=x$, it can be shown that $x$ is an asymptotically stable fixed point of $f$ (roughly: if you start near $x$, and iterate $f$, you converge to $x$) if $|f'(x)|\lt1$, and unstable if $|f'(x)|\gt1$. Things are more complicated if $|f'(x)|=1$ and, in the case $f'(x)=-1$, the determining factor is the value of the Schwarzian derivative evaluated at $x$. You can look up the Schwarzian derivative --- you'll find it involves $f'''(x)$.