Perturbation-induced emergence of Poisson-like behavior in non-Poisson systems

Abstract

The response of a system with ON–OFF intermittency to an external harmonicperturbation is discussed. ON–OFF intermittency is described by means of a sequence ofrandom events, i.e., the transitions from the ON to the OFF state and vice versa. Theunperturbed waiting times (WTs) between two events are assumed to satisfy arenewal condition, i.e., the WTs are statistically independent random variables.The response of a renewal model with non-Poisson ON–OFF intermittency, associated withnon-exponential WT distribution, is analyzed by looking at the changes induced in the WTstatistical distribution by the harmonic perturbation. The scaling properties are alsostudied by means of diffusion entropy analysis.It is found that, in the range of fast and relatively strong perturbation, the non-Poissonsystem displays a Poisson-like behavior in both WT distribution and scaling.In particular, the histogram of perturbed WTs becomes a sequence of equallyspaced peaks, with intensity decaying exponentially in time. Further, the diffusionentropy detects an ordinary scaling (related to normal diffusion) instead of theexpected unperturbed anomalous scaling related to the inverse power-law decay.Thus, an analysis based on the WT histogram and/or on scaling methods has to beconsidered with some care when dealing with perturbed intermittent systems.