Chaos in Discrete Systems and Diagnosis of Experimental Chaos

Tohru KOHDA  Kazuyuki AIHARA  

IEICE TRANSACTIONS (1976-1990)   Vol.E73   No.6   pp.772-783
Publication Date: 1990/06/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: INVITED PAPER (Special Issue on Engineering Chaos)

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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.