Large Fluctuations in the StationaryNonstationary Chaos Transition
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Abstract
Dynamical aspects of the transition process between stationary and nonstaionary chaos are numerically studied using the modified Bernoulli map. It was shown in a previous paper that the mean path of those transient processes reveals a universal logarithmic scaling of the renewal function, though there appear very large fluctuations around the mean path. First, we demonstrate the universal features of fluctuating transient paths. Next, we propose a new statistical quantity to describe the maximum fluctuation, and characterize the detailed structure of the logarithmic scaling in terms of the distribution of these quantities. The main point of the present paper is to report that large fluctuations obey two statistical laws, the Weibull and LogWeibull distributions, and that the crossover of both distributions is the universal phenomenon in the modified Bernoulli systems independent of the details of the mechanism which induces the stationarynonstationary transition. We also discuss a seismological law in relation to the universality of the large fluctuations in the stationarynonstationary chaos transition.
Journal

 Progress of Theoretical Physics

Progress of Theoretical Physics 114(4), 737748, 200510
Published for the Yukawa Institute for Theoretical Physics and the Physical Society of Japan