Basin of Attraction through Invariant Curves and Dominant Functions
We study a second-order difference equation of the form z<inf>n+1</inf> = z<inf>n</inf> F (z<inf>n-1</inf>) + h, where both F (z) and z F (z) are decreasing. We consider a set of invariant curves at h = 1 and use it to characterize the behaviour of solutions when...
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2015
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| Online Access: | http://hdl.handle.net/20.500.12458/33 https://www.scopus.com/inward/record.uri?eid=2-s2.0-84935863343&doi=10.1155%2f2015%2f160672&partnerID=40&md5=bad8e926eda0eac68463f6ca1d11565c |
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| _version_ | 1857415064750915584 |
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| author | Alsharawi, Ziyad |
| author2 | Al-Ghassani, Asma Amleh, Amal |
| author2_role | author author |
| author_facet | Alsharawi, Ziyad Al-Ghassani, Asma Amleh, Amal |
| author_role | author |
| dc.creator.none.fl_str_mv | Alsharawi, Ziyad Al-Ghassani, Asma Amleh, Amal |
| dc.date.none.fl_str_mv | 2015 2018-10-21T10:50:44Z 2018-10-21T10:50:44Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | 1026-0226 http://hdl.handle.net/20.500.12458/33 10.1155/2015/160672 2-s2.0-84935863343 https://www.scopus.com/inward/record.uri?eid=2-s2.0-84935863343&doi=10.1155%2f2015%2f160672&partnerID=40&md5=bad8e926eda0eac68463f6ca1d11565c |
| dc.language.none.fl_str_mv | en |
| dc.publisher.none.fl_str_mv | Hindawi Publishing Corporation |
| dc.relation.none.fl_str_mv | Discrete Dynamics in Nature and Society 2015 |
| dc.title.none.fl_str_mv | Basin of Attraction through Invariant Curves and Dominant Functions |
| dc.type.none.fl_str_mv | Controlled Vocabulary for Resource Type Genres::text::periodical::journal::contribution to journal::journal article |
| description | We study a second-order difference equation of the form z<inf>n+1</inf> = z<inf>n</inf> F (z<inf>n-1</inf>) + h, where both F (z) and z F (z) 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. © 2015 Ziyad AlSharawi et al. |
| id | sorbonner_96c4cb9e6c91d7706961ff058b4838d1 |
| identifier_str_mv | 1026-0226 10.1155/2015/160672 2-s2.0-84935863343 |
| language_invalid_str_mv | en |
| network_acronym_str | sorbonner |
| network_name_str | Sorbonne University Abu Dhabi repository |
| oai_identifier_str | oai:depot.sorbonne.ae:20.500.12458/33 |
| publishDate | 2015 |
| publisher.none.fl_str_mv | Hindawi Publishing Corporation |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Basin of Attraction through Invariant Curves and Dominant FunctionsAlsharawi, ZiyadAl-Ghassani, AsmaAmleh, AmalWe study a second-order difference equation of the form z<inf>n+1</inf> = z<inf>n</inf> F (z<inf>n-1</inf>) + h, where both F (z) and z F (z) 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. © 2015 Ziyad AlSharawi et al.Hindawi Publishing Corporation2018-10-21T10:50:44Z2018-10-21T10:50:44Z2015Controlled Vocabulary for Resource Type Genres::text::periodical::journal::contribution to journal::journal articleapplication/pdf1026-0226http://hdl.handle.net/20.500.12458/3310.1155/2015/1606722-s2.0-84935863343https://www.scopus.com/inward/record.uri?eid=2-s2.0-84935863343&doi=10.1155%2f2015%2f160672&partnerID=40&md5=bad8e926eda0eac68463f6ca1d11565cenDiscrete Dynamics in Nature and Society2015oai:depot.sorbonne.ae:20.500.12458/332024-02-05T06:31:48Z |
| spellingShingle | Basin of Attraction through Invariant Curves and Dominant Functions Alsharawi, Ziyad |
| 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/20.500.12458/33 https://www.scopus.com/inward/record.uri?eid=2-s2.0-84935863343&doi=10.1155%2f2015%2f160672&partnerID=40&md5=bad8e926eda0eac68463f6ca1d11565c |