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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 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.

Journal

  • Progress of Theoretical Physics

    Progress of Theoretical Physics 114(4), 737-748, 2005-10

    Published for the Yukawa Institute for Theoretical Physics and the Physical Society of Japan

Cited by:  2

Codes

  • NII Article ID (NAID)
    110002250959
  • NII NACSIS-CAT ID (NCID)
    AA00791455
  • Text Lang
    ENG
  • Article Type
    Journal Article
  • ISSN
    0033068X
  • NDL Article ID
    7676817
  • NDL Source Classification
    ZM35(科学技術--物理学)
  • NDL Call No.
    Z53-A468
  • Data Source
    CJPref  NDL  NII-ELS 
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