Chaos in Discrete Systems and Diagnosis of Experimental Chaos

Tohru KOHDA; Kazuyuki AIHARA

Chaos in Discrete Systems and Diagnosis of Experimental Chaos

Tohru KOHDA, Kazuyuki AIHARA

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A review is presented of the definitions of 'chaos' in the discrete system, the diagnosing methods of chaotic systems, and examples of engineering and/or biological chaos. First, enumerating physically intuitive pictures of one-dimensional chaos shows that there are many possible definitions of 'chaos' and that the 'observable chaos' is an important concept. Important roles of the Frobenius-Perron operator are discussed in theoretically studying statistical quantities of a completely chaotic orbit. In order to measure chaos, several quantities of a strange attractor are listed. Some of chaotic maps are shown to be applicable to a pseudorandom number generator. To examine biological chaos, macroscopic analyses and microscopic ones well be reviewed.

Publication: IEICE TRANSACTIONS on transactions Vol.E73-E No.6 pp.772-783

Publication Date: 1990/06/25

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Type of Manuscript: Special Section INVITED PAPER (Special Issue on Engineering Chaos)

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Tohru KOHDA
Kazuyuki AIHARA

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Tohru KOHDA, Kazuyuki AIHARA, "Chaos in Discrete Systems and Diagnosis of Experimental Chaos" in IEICE TRANSACTIONS on transactions, vol. E73-E, no. 6, pp. 772-783, June 1990, doi: .
Abstract: A review is presented of the definitions of 'chaos' in the discrete system, the diagnosing methods of chaotic systems, and examples of engineering and/or biological chaos. First, enumerating physically intuitive pictures of one-dimensional chaos shows that there are many possible definitions of 'chaos' and that the 'observable chaos' is an important concept. Important roles of the Frobenius-Perron operator are discussed in theoretically studying statistical quantities of a completely chaotic orbit. In order to measure chaos, several quantities of a strange attractor are listed. Some of chaotic maps are shown to be applicable to a pseudorandom number generator. To examine biological chaos, macroscopic analyses and microscopic ones well be reviewed.
URL: https://globals.ieice.org/en_transactions/transactions/10.1587/e73-e_6_772/_p

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@ARTICLE{e73-e_6_772,
author={Tohru KOHDA, Kazuyuki AIHARA, },
journal={IEICE TRANSACTIONS on transactions},
title={Chaos in Discrete Systems and Diagnosis of Experimental Chaos},
year={1990},
volume={E73-E},
number={6},
pages={772-783},
abstract={A review is presented of the definitions of 'chaos' in the discrete system, the diagnosing methods of chaotic systems, and examples of engineering and/or biological chaos. First, enumerating physically intuitive pictures of one-dimensional chaos shows that there are many possible definitions of 'chaos' and that the 'observable chaos' is an important concept. Important roles of the Frobenius-Perron operator are discussed in theoretically studying statistical quantities of a completely chaotic orbit. In order to measure chaos, several quantities of a strange attractor are listed. Some of chaotic maps are shown to be applicable to a pseudorandom number generator. To examine biological chaos, macroscopic analyses and microscopic ones well be reviewed.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - Chaos in Discrete Systems and Diagnosis of Experimental Chaos
T2 - IEICE TRANSACTIONS on transactions
SP - 772
EP - 783
AU - Tohru KOHDA
AU - Kazuyuki AIHARA
PY - 1990
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E73-E
IS - 6
JA - IEICE TRANSACTIONS on transactions
Y1 - June 1990
AB - A review is presented of the definitions of 'chaos' in the discrete system, the diagnosing methods of chaotic systems, and examples of engineering and/or biological chaos. First, enumerating physically intuitive pictures of one-dimensional chaos shows that there are many possible definitions of 'chaos' and that the 'observable chaos' is an important concept. Important roles of the Frobenius-Perron operator are discussed in theoretically studying statistical quantities of a completely chaotic orbit. In order to measure chaos, several quantities of a strange attractor are listed. Some of chaotic maps are shown to be applicable to a pseudorandom number generator. To examine biological chaos, macroscopic analyses and microscopic ones well be reviewed.
ER -