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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |