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

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Abstract

<p>The response of a system with ON–OFF intermittency to an external<br>\nharmonic perturbation is discussed. ON–OFF intermittency is described by<br>\nmeans of a sequence of random events, i.e., the transitions from the ON to the<br>\nOFF state and vice versa. The unperturbed waiting times (WTs) between two<br>\nevents are assumed to satisfy a renewal condition, i.e., the WTs are statistically<br>\nindependent random variables.<br>\nThe response of a renewal model with non-Poisson ON–OFF intermittency,<br>\nassociated with non-exponential WT distribution, is analyzed by looking at the<br>\nchanges induced in the WT statistical distribution by the harmonic perturbation.<br>\nThe scaling properties are also studied by means of diffusion entropy analysis.<br>\nIt is found that, in the range of fast and relatively strong perturbation, the<br>\nnon-Poisson system displays a Poisson-like behavior in both WT distribution and<br>\nscaling. In particular, the histogram of perturbed WTs becomes a sequence of<br>\nequally spaced peaks, with intensity decaying exponentially in time. Further, the<br>\ndiffusion entropy detects an ordinary scaling (related to normal diffusion) instead<br>\nof the expected unperturbed anomalous scaling related to the inverse power-law<br>\ndecay.</p>

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