Rounding Logistic Maps over Integers and the Properties of the Generated Sequences

Takeru MIYAZAKI  Shunsuke ARAKI  Yasuyuki NOGAMI  Satoshi UEHARA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.9   pp.1817-1825
Publication Date: 2011/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.1817
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory
Keyword: 
logistic maps over integers,  rounding,  period,  link length,  

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Summary: 
Because of its simple structure, many reports on the logistic map have been presented. To implement this map on computers, finite precision is usually used, and therefore rounding is required. There are five major methods to implement rounding, but, to date, no study of rounding applied to the logistic map has been reported. In the present paper, we present experimental results showing that the properties of sequences generated by the logistic map are heavily dependent on the rounding method used and give a theoretical analysis of each method. Then, we describe why using the map with a floor function for rounding generates long aperiodic subsequences.