I'd suggest an interactive exhibit where people can tweak the parameters of a population model with 3 species in it. Have an information panel which explains what the parameters represent. Suggest goals such as (1) keep the rabbits from going extinct, (2) create a stable equilibrium where all three species survive, (3) find a cyclic solution, etc. Experts could probably come up with a good system that exhibited lots of interesting behavior. Let people visualize their solutions both graphically (3-D graph of all three populations as well as 2-D graphs of any two populations of their choosing). There are probably other clever graphical representations that others could come up with as well.

Overall, I think this is a great endeavor and I hope that you will focus on making the exhibits interactive, with pathways to learning. Ideally, the same person could visit an exhibit a half dozen times and learn something new each time. Of course, making things fun and interesting is really important too - but I think that should naturally emerge from the design of interactive ways to explore a beautiful piece of mathematics.