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Acta Mathematica Sinica, English Series

, Volume 34, Issue 5, pp 891–900 | Cite as

On the Periodic Logistic Map

  • Cui Ping Li
  • Ming Zhao
Article
  • 40 Downloads

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 map
$${x_{n + 1}} = {r_n}{x_n}\left( {1 - {x_n}} \right),n = 0,1, \ldots ,$$
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.

Keywords

Non-autonomous logistic map periodic orbit asymptotic stable 

MR(2010) Subject Classification

37B55 37C05 37E05 

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Copyright information

© 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 2017

Authors and Affiliations

  1. 1.LMIB-School of Mathematics and Systems ScienceBeihang UniversityBeijingP. R. China

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