Is there a relationship between computational complexity theory and complex systems theory?
This paper by Kanter, Kopelowitz, and  Kinzel, Public Channel Cryptography: Chaos Synchronization and Hilbert’s Tenth Problem shows that there is a strong connection between nonlinear dynamics and NP-complete problems with the promise of novel secure public-channel protocols.

Phys. Rev. Lett. 101, 084102 (2008)