Deterministic Bak-Sneppen model. Lyapunov spectrum and avalanches as return times

Abstract

A deterministic version of the Bak-Sneppen model is studied. The role of the Lyapunov spectrum in the onset of scale-free behavior is established and avalanches are interpreted as return times to a zero-measure set. The problem of accurate determination of the scaling exponents near the critical barrier is addressed using a characteristic function approach. A general equation for return times to a small measure set is established and used to obtain information on the nature of Bak-Sneppen dynamics.