1994 Fiscal Year Final Research Report Summary
Analysis of Chaotic Fluctuations Based on New Statistical Theory and Its Apphlications to Physical Systems
| Project/Area Number |
05836024
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
非線形科学
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| Research Institution | KYUSHU UNIVERSITY |
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Principal Investigator |
FUJISAKA Hirokazu Kyushu Univ.Facul.of Science, Assoc.Prof., 理学部, 助教授 (40156849)
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| Project Period (FY) |
1993 – 1994
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| Keywords | Large deviation statistics / Intermittency / Periodic cycle expansion / Glassy pattern / Multifractal |
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| Research Abstract |
1.One of eminent characteristics of chaotic fluctuations is that they are highly different from Gaussian noise, reflecting deterministic nature of chaos. In this study we developed a new method to analyze such highly non-Gaussian time series by employing the large deviation theory, and applied it to physical systems. Near the type-I intermittency transition pont we succeeded to single out burst and laminar motions separately, and found a new anomalous statistical behavior which cannot be found with an ordinary analysis. We further proposed a continued-fraction epansion for large deviation statistics. It is found that the approximation become more appropriate by increasing the period of the unstable periodic orbits.
2.We found that a spatially distributed dynamical system exhibits a new type of motion which is spatially random and temporally periodic, observed after a long transient process for random initial candtion. This was called "dynamical glass". It was found that dynamical glass is a uniquituous phenomenon observed in a wide range of dissipative, coupled oscillator systems, and the necessity condition for the appearance of dynamical glass is clarified. We further studied the distribution of duration of formation process of glassy state, and found that multifractal property holds.
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