COMPLEX CHAOTIC SYSTEMS AND EMERGENT PHENOMENA

Chaos is a complex behavioural pattern associated with nonlinear syste ms. Its association with the analytical complexity of the generating s ystem is thought to be minimal. Our experiments show that this is not necessarily true and that, with the increase of analytical complexity, newer classes of dynamical behaviour can be seen. We call these new c lasses emergent because the system we study remains the same so far as the physics it represents is concerned, while we apply methods to inc rease intrinsically its degrees of freedom. We propose four techniques for the latter: (complex)ification, splitting, signal-flow-graph prod ucts, and interpolation/extrapolation. Some interesting new behavioura l patterns which emerge experimentally and which we report here are: a ttractor symmetries, duality between time and parameters, and a purpor tedly new route to chaos, named after Gibbs.