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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 4682168, 6 pages
http://dx.doi.org/10.1155/2016/4682168
Research Article

Number of Forts in Iterated Logistic Mapping

1Chengdu Radio and TV University, Chengdu, Sichuan 610051, China
2Chengdu Technological University, Chengdu, Sichuan 611730, China

Received 15 May 2016; Accepted 17 August 2016

Academic Editor: Daniele Fournier-Prunaret

Copyright © 2016 Kaixuan Yu and Zhiheng Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using the theory of complete discrimination system and the computer algebra system MAPLE V.17, we compute the number of forts for the logistic mapping on parameterized by . We prove that if then the number of forts does not increase under iteration and that if then the number of forts is not bounded under iteration. Furthermore, we focus on the case of and give for each some critical values of for the change of numbers of forts.