On the Periodic Logistic Map

Cui Ping Li; Ming Zhao

doi:10.1007/s10114-017-6011-z

On the Periodic Logistic Map

Cui Ping Li^*
, Ming Zhao

^*此作品的通讯作者

数学科学学院

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

In this paper, the famous logistic map is studied in a new point of view. We study the boundedness and the periodicity of non-autonomous logistic mapxn+1=rnxn(1−xn),n=0,1,…, where r_n is a positive p-periodic sequence. The sufficient conditions are given to support the existence of asymptotically stable and unstable p-periodic orbits. This appears to be the first study of the map with variable parameter r.

源语言	英语
页（从-至）	891-900
页数	10
期刊	Acta Mathematica Sinica, English Series
卷	34
期	5
DOI	https://doi.org/10.1007/s10114-017-6011-z
出版状态	已出版 - 1 5月 2018

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title = "On the Periodic Logistic Map",

abstract = "In this paper, the famous logistic map is studied in a new point of view. We study the boundedness and the periodicity of non-autonomous logistic mapxn+1=rnxn(1−xn),n=0,1,…, where rn is a positive p-periodic sequence. The sufficient conditions are given to support the existence of asymptotically stable and unstable p-periodic orbits. This appears to be the first study of the map with variable parameter r.",

keywords = "Non-autonomous logistic map, asymptotic stable, periodic orbit",

author = "Li, \{Cui Ping\} and Ming Zhao",

note = "Publisher Copyright: {\textcopyright} 2017, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2018",

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doi = "10.1007/s10114-017-6011-z",

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TY - JOUR

T1 - On the Periodic Logistic Map

AU - Li, Cui Ping

AU - Zhao, Ming

N1 - Publisher Copyright: © 2017, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - In this paper, the famous logistic map is studied in a new point of view. We study the boundedness and the periodicity of non-autonomous logistic mapxn+1=rnxn(1−xn),n=0,1,…, where rn is a positive p-periodic sequence. The sufficient conditions are given to support the existence of asymptotically stable and unstable p-periodic orbits. This appears to be the first study of the map with variable parameter r.

AB - In this paper, the famous logistic map is studied in a new point of view. We study the boundedness and the periodicity of non-autonomous logistic mapxn+1=rnxn(1−xn),n=0,1,…, where rn is a positive p-periodic sequence. The sufficient conditions are given to support the existence of asymptotically stable and unstable p-periodic orbits. This appears to be the first study of the map with variable parameter r.

KW - Non-autonomous logistic map

KW - asymptotic stable

KW - periodic orbit

UR - https://www.scopus.com/pages/publications/85031508644

U2 - 10.1007/s10114-017-6011-z

DO - 10.1007/s10114-017-6011-z

M3 - 文章

AN - SCOPUS:85031508644

SN - 1439-8516

VL - 34

SP - 891

EP - 900

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 5

ER -

On the Periodic Logistic Map

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