Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity
In this paper, we consider nonautonomous second order difference equations of the form xn+1 = F(n, xn, xn−1), where F is p-periodic in its first component, non-decreasing in its second component and non-increasing in its third component. The map F is referred to as periodic of mixed monotonicity, wh...
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| المؤلف الرئيسي: | |
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| التنسيق: | article |
| منشور في: |
2022
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/23576 |
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| _version_ | 1864513442828779520 |
|---|---|
| author | Al-Sharawi, Ziyad |
| author_facet | Al-Sharawi, Ziyad |
| author_role | author |
| dc.creator.none.fl_str_mv | Al-Sharawi, Ziyad |
| dc.date.none.fl_str_mv | 2022-04-08T05:24:30Z 2022-04-08T05:24:30Z 2022-02 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | AlSharawi, Z. (2022). Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity. In Chaos, Solitons & Fractals (Vol. 157, p. 111933). Elsevier BV. https://doi.org/10.1016/j.chaos.2022.111933 0960-0779 http://hdl.handle.net/11073/23576 10.1016/j.chaos.2022.111933 |
| 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.chaos.2022.111933 |
| dc.subject.none.fl_str_mv | Mixed monotonicity Global stability Embedding Periodic maps Cycles Attractor |
| dc.title.none.fl_str_mv | Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity |
| dc.type.none.fl_str_mv | Peer-Reviewed Postprint info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | In this paper, we consider nonautonomous second order difference equations of the form xn+1 = F(n, xn, xn−1), where F is p-periodic in its first component, non-decreasing in its second component and non-increasing in its third component. The map F is referred to as periodic of mixed monotonicity, which broadens the notion of maps of mixed monotonicity. We introduce the concept of artificial cycles, and we develop the embedding technique to tackle periodicity and globally attracting cycles in periodic 2-dimensional maps of mixed monotonicity. We present a result on globally attracting cycles and demonstrate its application to periodic systems. The first application is a periodic rational difference equation of second order, and the second application is a population model with periodic stocking. In both cases, we prove the existence of a globally attracting cycle. |
| format | article |
| id | aus_7d0fd42d48bf7a071c7c4b4ba284115b |
| identifier_str_mv | AlSharawi, Z. (2022). Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity. In Chaos, Solitons & Fractals (Vol. 157, p. 111933). Elsevier BV. https://doi.org/10.1016/j.chaos.2022.111933 0960-0779 10.1016/j.chaos.2022.111933 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/23576 |
| publishDate | 2022 |
| publisher.none.fl_str_mv | Elsevier |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Embedding and global stability in periodic 2-dimensional maps of mixed monotonicityAl-Sharawi, ZiyadMixed monotonicityGlobal stabilityEmbeddingPeriodic mapsCyclesAttractorIn this paper, we consider nonautonomous second order difference equations of the form xn+1 = F(n, xn, xn−1), where F is p-periodic in its first component, non-decreasing in its second component and non-increasing in its third component. The map F is referred to as periodic of mixed monotonicity, which broadens the notion of maps of mixed monotonicity. We introduce the concept of artificial cycles, and we develop the embedding technique to tackle periodicity and globally attracting cycles in periodic 2-dimensional maps of mixed monotonicity. We present a result on globally attracting cycles and demonstrate its application to periodic systems. The first application is a periodic rational difference equation of second order, and the second application is a population model with periodic stocking. In both cases, we prove the existence of a globally attracting cycle.American University of SharjahElsevier2022-04-08T05:24:30Z2022-04-08T05:24:30Z2022-02Peer-ReviewedPostprintinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfAlSharawi, Z. (2022). Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity. In Chaos, Solitons & Fractals (Vol. 157, p. 111933). Elsevier BV. https://doi.org/10.1016/j.chaos.2022.1119330960-0779http://hdl.handle.net/11073/2357610.1016/j.chaos.2022.111933en_UShttps://doi.org/10.1016/j.chaos.2022.111933oai:repository.aus.edu:11073/235762024-08-22T12:02:02Z |
| spellingShingle | Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity Al-Sharawi, Ziyad Mixed monotonicity Global stability Embedding Periodic maps Cycles Attractor |
| status_str | publishedVersion |
| title | Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity |
| title_full | Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity |
| title_fullStr | Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity |
| title_full_unstemmed | Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity |
| title_short | Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity |
| title_sort | Embedding and global stability in periodic 2-dimensional maps of mixed monotonicity |
| topic | Mixed monotonicity Global stability Embedding Periodic maps Cycles Attractor |
| url | http://hdl.handle.net/11073/23576 |