IEICE TRANSACTIONS on Fundamentals
Rounding Logistic Maps over Integers and the Properties of the Generated Sequences
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.9 pp.1817-1825
- Publication Date
- 2011/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E94.A.1817
- Type of Manuscript
- PAPER
- Category
- Information Theory
Authors
Keyword
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Takeru MIYAZAKI, Shunsuke ARAKI, Yasuyuki NOGAMI, Satoshi UEHARA, "Rounding Logistic Maps over Integers and the Properties of the Generated Sequences" in IEICE TRANSACTIONS on Fundamentals,
vol. E94-A, no. 9, pp. 1817-1825, September 2011, doi: 10.1587/transfun.E94.A.1817.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.1817/_p
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@ARTICLE{e94-a_9_1817,
author={Takeru MIYAZAKI, Shunsuke ARAKI, Yasuyuki NOGAMI, Satoshi UEHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Rounding Logistic Maps over Integers and the Properties of the Generated Sequences},
year={2011},
volume={E94-A},
number={9},
pages={1817-1825},
abstract={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.},
keywords={},
doi={10.1587/transfun.E94.A.1817},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - Rounding Logistic Maps over Integers and the Properties of the Generated Sequences
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1817
EP - 1825
AU - Takeru MIYAZAKI
AU - Shunsuke ARAKI
AU - Yasuyuki NOGAMI
AU - Satoshi UEHARA
PY - 2011
DO - 10.1587/transfun.E94.A.1817
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2011
AB - 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.
ER -
English
