Basin of Attraction through Invariant Curves and Dominant Functions
We study a second-order difference equation of the form ₙ₊₁= ₙ(ₙ₋₁) + ℎ, where both () and () are decreasing. We consider a set of invariant curves at ℎ = 1 and use it to characterize the behaviour of solutions when ℎ > 1 and when 0 < ℎ < 1.The case ℎ > 1 is related to the Y2K problem. F...
محفوظ في:
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| مؤلفون آخرون: | , |
| التنسيق: | article |
| منشور في: |
2015
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| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/16678 |
| الوسوم: |
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| _version_ | 1864513437117186048 |
|---|---|
| author | Al-Sharawi, Ziyad |
| author2 | Al-Ghassani, Asma Amleh, Amal |
| author2_role | author author |
| author_facet | Al-Sharawi, Ziyad Al-Ghassani, Asma Amleh, Amal |
| author_role | author |
| dc.creator.none.fl_str_mv | Al-Sharawi, Ziyad Al-Ghassani, Asma Amleh, Amal |
| dc.date.none.fl_str_mv | 2015 2020-06-04T09:21:31Z 2020-06-04T09:21:31Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Basin of Attraction through Invariant Curves and Dominant FunctionsAlSharawi, Z., Al-Ghassani, A., and Amleh, A. M. (2015). Basin of attraction through invariant curves and dominant functions. Discrete Dynamics in Nature and Society, 2015. doi: 10.1155/2015/160672 1607-887X http://hdl.handle.net/11073/16678 10.1155/2015/160672 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | Hindawi |
| dc.relation.none.fl_str_mv | https://doi.org/10.1155/2015/160672 |
| dc.title.none.fl_str_mv | Basin of Attraction through Invariant Curves and Dominant Functions |
| dc.type.none.fl_str_mv | Peer-Reviewed Published version info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | We study a second-order difference equation of the form ₙ₊₁= ₙ(ₙ₋₁) + ℎ, where both () and () are decreasing. We consider a set of invariant curves at ℎ = 1 and use it to characterize the behaviour of solutions when ℎ > 1 and when 0 < ℎ < 1.The case ℎ > 1 is related to the Y2K problem. For 0 < ℎ < 1, we study the stability of the equilibrium solutions and find an invariant region where solutions are attracted to the stable equilibrium. In particular, for certain range of the parameters, a subset of the basin of attraction of the stable equilibrium is achieved by bounding positive solutions using the iteration of dominant functions with attracting equilibria. |
| format | article |
| id | aus_39b353e400ae9fdc6c1cfd5aa05747ee |
| identifier_str_mv | Basin of Attraction through Invariant Curves and Dominant FunctionsAlSharawi, Z., Al-Ghassani, A., and Amleh, A. M. (2015). Basin of attraction through invariant curves and dominant functions. Discrete Dynamics in Nature and Society, 2015. doi: 10.1155/2015/160672 1607-887X 10.1155/2015/160672 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/16678 |
| publishDate | 2015 |
| publisher.none.fl_str_mv | Hindawi |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Basin of Attraction through Invariant Curves and Dominant FunctionsAl-Sharawi, ZiyadAl-Ghassani, AsmaAmleh, AmalWe study a second-order difference equation of the form ₙ₊₁= ₙ(ₙ₋₁) + ℎ, where both () and () are decreasing. We consider a set of invariant curves at ℎ = 1 and use it to characterize the behaviour of solutions when ℎ > 1 and when 0 < ℎ < 1.The case ℎ > 1 is related to the Y2K problem. For 0 < ℎ < 1, we study the stability of the equilibrium solutions and find an invariant region where solutions are attracted to the stable equilibrium. In particular, for certain range of the parameters, a subset of the basin of attraction of the stable equilibrium is achieved by bounding positive solutions using the iteration of dominant functions with attracting equilibria.Hindawi2020-06-04T09:21:31Z2020-06-04T09:21:31Z2015Peer-ReviewedPublished versioninfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfBasin of Attraction through Invariant Curves and Dominant FunctionsAlSharawi, Z., Al-Ghassani, A., and Amleh, A. M. (2015). Basin of attraction through invariant curves and dominant functions. Discrete Dynamics in Nature and Society, 2015. doi: 10.1155/2015/1606721607-887Xhttp://hdl.handle.net/11073/1667810.1155/2015/160672en_UShttps://doi.org/10.1155/2015/160672oai:repository.aus.edu:11073/166782024-08-22T12:01:31Z |
| spellingShingle | Basin of Attraction through Invariant Curves and Dominant Functions Al-Sharawi, Ziyad |
| status_str | publishedVersion |
| title | Basin of Attraction through Invariant Curves and Dominant Functions |
| title_full | Basin of Attraction through Invariant Curves and Dominant Functions |
| title_fullStr | Basin of Attraction through Invariant Curves and Dominant Functions |
| title_full_unstemmed | Basin of Attraction through Invariant Curves and Dominant Functions |
| title_short | Basin of Attraction through Invariant Curves and Dominant Functions |
| title_sort | Basin of Attraction through Invariant Curves and Dominant Functions |
| url | http://hdl.handle.net/11073/16678 |