Real and Apparent Divergencies in Low-Frequency Spectra of Nonlinear Dynamical Systems

A. Ben-Mizrachi, I. Procaccia, N. Rosenberg, A. Schmidt, H.G. Schuster,

Physical Review A , vol 31, no 3, 1830-1840 (March 1985)

Abstract

We discuss apparent and real 1/fdelta divergencies in the small-frequency limit of power spectra of dynamical systems. Apparent 1/f2 divergencies appear in "type-I" intermittency and whenever there is infrequent random hopping between regions with chaotic motion. Real 1/fdelta divergencies appear in "type-II and -III" intermittency. The universal properties of these divergencies are discussed in the context of one- and two-dimensional maps.

1/f in dynamical system models