Large fluctuations in the stationary-nonstationary chaos transition

Takuma Akimoto*, Yoji Aizawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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 Log-Weibull distributions, and that the cross-over of both distributions is the universal phenomenon in the modified Bernoulli systems independent of the details of the mechanism which induces the stationary-nonstationary transition. We also discuss a seismological law in relation to the universality of the large fluctuations in the stationary-nonstationary chaos transition.

Original languageEnglish
Pages (from-to)737-748
Number of pages12
JournalProgress of Theoretical Physics
Issue number4
Publication statusPublished - 2005 Oct

ASJC Scopus subject areas

  • Physics and Astronomy(all)


Dive into the research topics of 'Large fluctuations in the stationary-nonstationary chaos transition'. Together they form a unique fingerprint.

Cite this