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

The response of a system with ON–OFF intermittency to an external
harmonic perturbation is discussed. ON–OFF intermittency is described by
means of a sequence of random events, i.e., the transitions from the ON to the
OFF state and vice versa. The unperturbed waiting times (WTs) between two
events are assumed to satisfy a renewal condition, i.e., the WTs are statistically
independent random variables.
The response of a renewal model with non-Poisson ON–OFF intermittency,
associated with non-exponential WT distribution, is analyzed by looking at the
changes induced in the WT statistical distribution by the harmonic perturbation.
The scaling properties are also studied by means of diffusion entropy analysis.
It is found that, in the range of fast and relatively strong perturbation, the
non-Poisson system displays a Poisson-like behavior in both WT distribution and
scaling. In particular, the histogram of perturbed WTs becomes a sequence of
equally spaced peaks, with intensity decaying exponentially in time. Further, the
diffusion entropy detects an ordinary scaling (related to normal diffusion) instead
of the expected unperturbed anomalous scaling related to the inverse power-law
decay.