Existence and stability of periodic orbits of periodic difference equations with delays
In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xₙ = f(n - 1, xₙ₋ₖ). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k...
محفوظ في:
| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | , |
| التنسيق: | article |
| منشور في: |
2008
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/16686 |
| الوسوم: |
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| _version_ | 1864513433992429568 |
|---|---|
| author | Al-Sharawi, Ziyad |
| author2 | Angelos, James Elaydi, Saber |
| author2_role | author author |
| author_facet | Al-Sharawi, Ziyad Angelos, James Elaydi, Saber |
| author_role | author |
| dc.creator.none.fl_str_mv | Al-Sharawi, Ziyad Angelos, James Elaydi, Saber |
| dc.date.none.fl_str_mv | 2008 2020-06-09T07:20:35Z 2020-06-09T07:20:35Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Alsharawi, Z., & Angelos, J., & Elaydi, S. (2008). Existence and stability of periodic orbits of periodic difference equations with delays. International Journal of Bifurcation and Chaos, 18(01), 203–217. https://doi.org/10.1142/S0218127408020239 1793-6551 http://hdl.handle.net/11073/16686 10.1142/S0218127408020239 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | World Scientific Publishing |
| dc.relation.none.fl_str_mv | https://doi.org/10.1142/S0218127408020239 |
| dc.subject.none.fl_str_mv | Periodic difference equations Periodic orbits Sharkovsky's theorem Global stability |
| dc.title.none.fl_str_mv | Existence and stability of periodic orbits of periodic difference equations with delays |
| dc.type.none.fl_str_mv | Peer-Reviewed Preprint info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xₙ = f(n - 1, xₙ₋ₖ). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of gcd(p, k) nonautonomous p/gcd(p, k)-periodic difference equations. We give formulas for calculating the number of different periodic orbits under certain conditions. In addition, when p and k are relatively prime integers, we introduce what we call the pk-Sharkovsky's ordering of the positive integers, and extend Sharkovsky's theorem to periodic difference equations with delays. Finally, we characterize global stability and show that the period of a globally asymptotically stable orbit must be divisible by p. |
| format | article |
| id | aus_1835819073dfcb12dfc981cac7b303b0 |
| identifier_str_mv | Alsharawi, Z., & Angelos, J., & Elaydi, S. (2008). Existence and stability of periodic orbits of periodic difference equations with delays. International Journal of Bifurcation and Chaos, 18(01), 203–217. https://doi.org/10.1142/S0218127408020239 1793-6551 10.1142/S0218127408020239 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/16686 |
| publishDate | 2008 |
| publisher.none.fl_str_mv | World Scientific Publishing |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Existence and stability of periodic orbits of periodic difference equations with delaysAl-Sharawi, ZiyadAngelos, JamesElaydi, SaberPeriodic difference equationsPeriodic orbitsSharkovsky's theoremGlobal stabilityIn this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xₙ = f(n - 1, xₙ₋ₖ). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of gcd(p, k) nonautonomous p/gcd(p, k)-periodic difference equations. We give formulas for calculating the number of different periodic orbits under certain conditions. In addition, when p and k are relatively prime integers, we introduce what we call the pk-Sharkovsky's ordering of the positive integers, and extend Sharkovsky's theorem to periodic difference equations with delays. Finally, we characterize global stability and show that the period of a globally asymptotically stable orbit must be divisible by p.World Scientific Publishing2020-06-09T07:20:35Z2020-06-09T07:20:35Z2008Peer-ReviewedPreprintinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfAlsharawi, Z., & Angelos, J., & Elaydi, S. (2008). Existence and stability of periodic orbits of periodic difference equations with delays. International Journal of Bifurcation and Chaos, 18(01), 203–217. https://doi.org/10.1142/S02181274080202391793-6551http://hdl.handle.net/11073/1668610.1142/S0218127408020239en_UShttps://doi.org/10.1142/S0218127408020239oai:repository.aus.edu:11073/166862024-08-22T12:01:58Z |
| spellingShingle | Existence and stability of periodic orbits of periodic difference equations with delays Al-Sharawi, Ziyad Periodic difference equations Periodic orbits Sharkovsky's theorem Global stability |
| status_str | publishedVersion |
| title | Existence and stability of periodic orbits of periodic difference equations with delays |
| title_full | Existence and stability of periodic orbits of periodic difference equations with delays |
| title_fullStr | Existence and stability of periodic orbits of periodic difference equations with delays |
| title_full_unstemmed | Existence and stability of periodic orbits of periodic difference equations with delays |
| title_short | Existence and stability of periodic orbits of periodic difference equations with delays |
| title_sort | Existence and stability of periodic orbits of periodic difference equations with delays |
| topic | Periodic difference equations Periodic orbits Sharkovsky's theorem Global stability |
| url | http://hdl.handle.net/11073/16686 |