CNLN: van der Pol
I have seen the van der Pol system in many papers, so probably most tools/tool authors have this example at their disposal:
x' = y
y' = (1 - x^2)*y - x
Is this interesting for the competition?
I think vanderpol can be a difficult benchmark depending on the initial states, unsafe states, and time bound. Can you propose two instances, one which is safe, and one which is unsafe?
Ideally it should be hard, but still possible for many tools to run the system.
The Van der Pol system might always be the first benchmark to test a reachability/invariant computation method on nonlinear dynamics. It is definitely interesting.
Why Hard?
Nearly all dynamics with limit cycles are hard to reachability computation. The flowpipe contruction methods may suffer from wrapping effect. If you could not find a fixed point in the first period then you probably may never find one. For invariant computation methods, only if you know the "template" of the limit cycle, the computation could be fast, but it also depends on the initial and unsafe sets in interest.
Why NOT Hard
You may always subdivide the state space for a 2-dimensional system to obtain a better accuracy. It's not expensive. Also you may have lots of heuristics ("only" work on 2D cases) to improve the performance and accuracy.