ABSTRACT
The features leading to deterministic chaos combined with a random noise are somewhat equivalent to a double randomness and we call “hyperchaos” such a situation. Indeed random-random walks in ordinary space, as diffusion in disordered systems, have shown a 1/f behavior. Thus, hyperchaos here introduced is a random-random walk in phase space, where in fact one of the two sources of complex behavior is due to the fractal structure arising from deterministic dynamics. To evaluate the impact of the following arguments, the author premises some historical remarks on 1/f spectra in nonlinear dynamics. The numerical evaluation of Arecchi et al 1984b and Arecchi et al 1985a showed that for some control parameters the boundary between basins of attraction was an intricated set of points, through which it was impossible to draw a simple line. A fundamental logical approach to the 1/f problem was based on the composition of a large number of Lorentzians whose weights are log-normally distributed.
