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

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 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.

Original language	English
Pages (from-to)	891-900
Number of pages	10
Journal	Acta Mathematica Sinica, English Series
Volume	34
Issue number	5
DOIs	https://doi.org/10.1007/s10114-017-6011-z
State	Published - 1 May 2018

Keywords

Non-autonomous logistic map
asymptotic stable
periodic orbit

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10.1007/s10114-017-6011-z

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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.",

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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

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DO - 10.1007/s10114-017-6011-z

M3 - 文章

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 5

ER -

On the Periodic Logistic Map

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