### 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 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 language | English |
---|---|

Pages (from-to) | 737-748 |

Number of pages | 12 |

Journal | Progress of Theoretical Physics |

Volume | 114 |

Issue number | 4 |

Publication status | Published - 2005 Oct |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical Physics*,

*114*(4), 737-748.

**Large fluctuations in the stationary-nonstationary chaos transition.** / Akimoto, Takuma; Aizawa, Yoji.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, vol. 114, no. 4, pp. 737-748.

}

TY - JOUR

T1 - Large fluctuations in the stationary-nonstationary chaos transition

AU - Akimoto, Takuma

AU - Aizawa, Yoji

PY - 2005/10

Y1 - 2005/10

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:29344468690

VL - 114

SP - 737

EP - 748

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 4

ER -