The effect of maps permutation on the global attractor of a periodic Beverton-Holt model
Consider a p-periodic difference equation xn+1 = fn(xn) with a global attractor. How does a permutation [fσ(p−1), . . . , fσ(1), fσ(0)] of the maps affect the global attractor? In this paper, we limit this general question to the Beverton-Holt model with p-periodic harvesting. We fix a set of harvestin...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | article |
| Published: |
2020
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/11073/16703 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1864513444159422464 |
|---|---|
| author | Al-Ghassani, Asma |
| author2 | Al-Sharawi, Ziyad |
| author2_role | author |
| author_facet | Al-Ghassani, Asma Al-Sharawi, Ziyad |
| author_role | author |
| dc.creator.none.fl_str_mv | Al-Ghassani, Asma Al-Sharawi, Ziyad |
| dc.date.none.fl_str_mv | 2020-06-15T11:39:41Z 2020-06-15T11:39:41Z 2020-04-01 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Al-Ghassani, A. S., & AlSharawi, Z. (2020). The effect of maps permutation on the global attractor of a periodic beverton-holt model. Applied Mathematics and Computation, 370. https://doi.org/10.1016/j.amc.2019.124905 1873-5649 http://hdl.handle.net/11073/16703 10.1016/j.amc.2019.124905 |
| 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.2019.124905 |
| dc.subject.none.fl_str_mv | Beverton-Holt Cycles Permutations Periodic harvesting Combinatorial dynamics |
| dc.title.none.fl_str_mv | The effect of maps permutation on the global attractor of a periodic Beverton-Holt model |
| dc.type.none.fl_str_mv | Peer-Reviewed Preprint info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | Consider a p-periodic difference equation xn+1 = fn(xn) with a global attractor. How does a permutation [fσ(p−1), . . . , fσ(1), fσ(0)] of the maps affect the global attractor? In this paper, we limit this general question to the Beverton-Holt model with p-periodic harvesting. We fix a set of harvesting quotas and give ourselves the liberty to permute them. The total harvesting yield is unchanged by the permutation, but the population geometric-mean may fluctuate. We investigate this notion and characterize the cases in which a permutation of the harvesting quotas has no effect or tangible effect on the population geometric-mean. In particular, as long as persistence is assured, all permutations within the dihedral group give same population geometric-mean. Other permutations may change the population geometric-mean. A characterization theorem has been obtained based on block reflections in the harvesting quotas. Finally, we associate directed graphs to the various permutations, then give the complete characterization when the periodicity of the system is four or five. |
| format | article |
| id | aus_ad348ea81c71c5476cc5cbed242bb3da |
| identifier_str_mv | Al-Ghassani, A. S., & AlSharawi, Z. (2020). The effect of maps permutation on the global attractor of a periodic beverton-holt model. Applied Mathematics and Computation, 370. https://doi.org/10.1016/j.amc.2019.124905 1873-5649 10.1016/j.amc.2019.124905 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/16703 |
| publishDate | 2020 |
| publisher.none.fl_str_mv | Elsevier |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | The effect of maps permutation on the global attractor of a periodic Beverton-Holt modelAl-Ghassani, AsmaAl-Sharawi, ZiyadBeverton-HoltCyclesPermutationsPeriodic harvestingCombinatorial dynamicsConsider a p-periodic difference equation xn+1 = fn(xn) with a global attractor. How does a permutation [fσ(p−1), . . . , fσ(1), fσ(0)] of the maps affect the global attractor? In this paper, we limit this general question to the Beverton-Holt model with p-periodic harvesting. We fix a set of harvesting quotas and give ourselves the liberty to permute them. The total harvesting yield is unchanged by the permutation, but the population geometric-mean may fluctuate. We investigate this notion and characterize the cases in which a permutation of the harvesting quotas has no effect or tangible effect on the population geometric-mean. In particular, as long as persistence is assured, all permutations within the dihedral group give same population geometric-mean. Other permutations may change the population geometric-mean. A characterization theorem has been obtained based on block reflections in the harvesting quotas. Finally, we associate directed graphs to the various permutations, then give the complete characterization when the periodicity of the system is four or five.Elsevier2020-06-15T11:39:41Z2020-06-15T11:39:41Z2020-04-01Peer-ReviewedPreprintinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfAl-Ghassani, A. S., & AlSharawi, Z. (2020). The effect of maps permutation on the global attractor of a periodic beverton-holt model. Applied Mathematics and Computation, 370. https://doi.org/10.1016/j.amc.2019.1249051873-5649http://hdl.handle.net/11073/1670310.1016/j.amc.2019.124905en_UShttps://doi.org/10.1016/j.amc.2019.124905oai:repository.aus.edu:11073/167032024-08-22T12:02:12Z |
| spellingShingle | The effect of maps permutation on the global attractor of a periodic Beverton-Holt model Al-Ghassani, Asma Beverton-Holt Cycles Permutations Periodic harvesting Combinatorial dynamics |
| status_str | publishedVersion |
| title | The effect of maps permutation on the global attractor of a periodic Beverton-Holt model |
| title_full | The effect of maps permutation on the global attractor of a periodic Beverton-Holt model |
| title_fullStr | The effect of maps permutation on the global attractor of a periodic Beverton-Holt model |
| title_full_unstemmed | The effect of maps permutation on the global attractor of a periodic Beverton-Holt model |
| title_short | The effect of maps permutation on the global attractor of a periodic Beverton-Holt model |
| title_sort | The effect of maps permutation on the global attractor of a periodic Beverton-Holt model |
| topic | Beverton-Holt Cycles Permutations Periodic harvesting Combinatorial dynamics |
| url | http://hdl.handle.net/11073/16703 |