On the periodic logistic equation
We show that the -periodic logistic equation ₙ₊₁ = μₙ mod ₙ(1 - ₙ) has cycles (periodic solutions) of minimal periods 1; ; 2; 3; …. Then we extend Singer’s theorem to periodic difference equations, and use it to show the -periodic logistic equation has at most stable cycles. Also, we present computa...
محفوظ في:
| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | |
| التنسيق: | article |
| منشور في: |
2006
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/16689 |
| الوسوم: |
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| _version_ | 1864513440730578944 |
|---|---|
| author | Al-Sharawi, Ziyad |
| author2 | Angelos, James |
| author2_role | author |
| author_facet | Al-Sharawi, Ziyad Angelos, James |
| author_role | author |
| dc.creator.none.fl_str_mv | Al-Sharawi, Ziyad Angelos, James |
| dc.date.none.fl_str_mv | 2006 2020-06-09T08:01:03Z 2020-06-09T08:01:03Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Alsharawi, Z., & Angelos, J. (2007). On the periodic logistic equation. Applied Mathematics and Computation, 180(1), 342. https://doi.org/10.1016/j.amc.2005.12.016 0096-3003 http://hdl.handle.net/11073/16689 10.1016/j.amc.2005.12.016 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | Elsevier |
| dc.relation.none.fl_str_mv | https://doi.org/10.1016/j.amc.2005.12.016 |
| dc.subject.none.fl_str_mv | Logistic map Non-autonomous Periodic solutions Singer’s theorem Attractors |
| dc.title.none.fl_str_mv | On the periodic logistic equation |
| dc.type.none.fl_str_mv | Peer-Reviewed Preprint info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | We show that the -periodic logistic equation ₙ₊₁ = μₙ mod ₙ(1 - ₙ) has cycles (periodic solutions) of minimal periods 1; ; 2; 3; …. Then we extend Singer’s theorem to periodic difference equations, and use it to show the -periodic logistic equation has at most stable cycles. Also, we present computational methods investigating the stable cycles in case = 2 and 3. |
| format | article |
| id | aus_04b2297ac79433a68387d99da3a7cebf |
| identifier_str_mv | Alsharawi, Z., & Angelos, J. (2007). On the periodic logistic equation. Applied Mathematics and Computation, 180(1), 342. https://doi.org/10.1016/j.amc.2005.12.016 0096-3003 10.1016/j.amc.2005.12.016 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/16689 |
| publishDate | 2006 |
| publisher.none.fl_str_mv | Elsevier |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | On the periodic logistic equationAl-Sharawi, ZiyadAngelos, JamesLogistic mapNon-autonomousPeriodic solutionsSinger’s theoremAttractorsWe show that the -periodic logistic equation ₙ₊₁ = μₙ mod ₙ(1 - ₙ) has cycles (periodic solutions) of minimal periods 1; ; 2; 3; …. Then we extend Singer’s theorem to periodic difference equations, and use it to show the -periodic logistic equation has at most stable cycles. Also, we present computational methods investigating the stable cycles in case = 2 and 3.Elsevier2020-06-09T08:01:03Z2020-06-09T08:01:03Z2006Peer-ReviewedPreprintinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfAlsharawi, Z., & Angelos, J. (2007). On the periodic logistic equation. Applied Mathematics and Computation, 180(1), 342. https://doi.org/10.1016/j.amc.2005.12.0160096-3003http://hdl.handle.net/11073/1668910.1016/j.amc.2005.12.016en_UShttps://doi.org/10.1016/j.amc.2005.12.016oai:repository.aus.edu:11073/166892024-08-22T12:01:43Z |
| spellingShingle | On the periodic logistic equation Al-Sharawi, Ziyad Logistic map Non-autonomous Periodic solutions Singer’s theorem Attractors |
| status_str | publishedVersion |
| title | On the periodic logistic equation |
| title_full | On the periodic logistic equation |
| title_fullStr | On the periodic logistic equation |
| title_full_unstemmed | On the periodic logistic equation |
| title_short | On the periodic logistic equation |
| title_sort | On the periodic logistic equation |
| topic | Logistic map Non-autonomous Periodic solutions Singer’s theorem Attractors |
| url | http://hdl.handle.net/11073/16689 |