Number of Forts in Iterated Logistic Mapping
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 fλ(x)=λx(1-x) on [0,1] parameterized by λ∈(0,4]. We prove that if 0<λ≤2 then the number of forts does not increase under iteration and that if λ&g...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/4682168 |
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doaj-b9346ff0f5d54cbd8ae0432a835516a82020-11-24T22:28:10ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/46821684682168Number of Forts in Iterated Logistic MappingKaixuan Yu0Zhiheng Yu1Chengdu Radio and TV University, Chengdu, Sichuan 610051, ChinaChengdu Technological University, Chengdu, Sichuan 611730, ChinaUsing the theory of complete discrimination system and the computer algebra system MAPLE V.17, we compute the number of forts for the logistic mapping fλ(x)=λx(1-x) on [0,1] parameterized by λ∈(0,4]. We prove that if 0<λ≤2 then the number of forts does not increase under iteration and that if λ>2 then the number of forts is not bounded under iteration. Furthermore, we focus on the case of λ>2 and give for each k=1,…,7 some critical values of λ for the change of numbers of forts.http://dx.doi.org/10.1155/2016/4682168 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Kaixuan Yu Zhiheng Yu |
| spellingShingle |
Kaixuan Yu Zhiheng Yu Number of Forts in Iterated Logistic Mapping Discrete Dynamics in Nature and Society |
| author_facet |
Kaixuan Yu Zhiheng Yu |
| author_sort |
Kaixuan Yu |
| title |
Number of Forts in Iterated Logistic Mapping |
| title_short |
Number of Forts in Iterated Logistic Mapping |
| title_full |
Number of Forts in Iterated Logistic Mapping |
| title_fullStr |
Number of Forts in Iterated Logistic Mapping |
| title_full_unstemmed |
Number of Forts in Iterated Logistic Mapping |
| title_sort |
number of forts in iterated logistic mapping |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1026-0226 1607-887X |
| publishDate |
2016-01-01 |
| description |
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 fλ(x)=λx(1-x) on [0,1] parameterized by λ∈(0,4]. We prove that if 0<λ≤2 then the number of forts does not increase under iteration and that if λ>2 then the number of forts is not bounded under iteration. Furthermore, we focus on the case of λ>2 and give for each k=1,…,7 some critical values of λ for the change of numbers of forts. |
| url |
http://dx.doi.org/10.1155/2016/4682168 |
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