http://www.scholarpedia.org/article/Hyperchaos#Experimental_hyperchaotic_behaviors

and some more pointers:

* C. Stan, C.P. Cristescu, and D. Alexandroaei, Chaos and hyperchaos in a symmetrical discharge plasma: experiment and modelling, University Politehnica Of Bucharest Scientific Bulletin-Series A-Applied Mathematics And Physics, vol. 70 (4), 25-30 (2008).

* R. Stoop et al., A p-Ge semiconductor experiment showing chaos and hyperchaos, Physica D, vol. 35 (3), 425-435 (1989).

* T. Matsumoto, L. Chua, and K. Kobayashi, Hyperchaos - Laboratory experiment and numerical confirmation, IEEE Transactions On Circuits And Systems, vol. 33 (11), 1143-1147 (1986).