Modelos discretos para agregação populacional
Autor(a) principal: | |
---|---|
Data de Publicação: | 2019 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional Manancial UFSM |
Texto Completo: | http://repositorio.ufsm.br/handle/1/19763 |
Resumo: | The mechanisms that can lead to the formation of heterogeneous distribution of individuals of many biological species arouse the interest of researchers from various areas. Many mathematical models of pattern formation are based on the Turing mechanism and on aggregation processes in relation to concentration gradients of a chemical substance. Recently, the Cahn-Hilliard principle of phase separation, which assumes density-dependent movement, has been used to study self-organized mussel patterns. In this work, we formulate three discrete models of coupled map networks with density-dependent movement to describe processes of aggregation and formation of spatial patterns. Some species show better development at intermediate densities, avoiding problems related to overpopulation or the difficulty of keeping the species at low population densities. Thus, the first model considers only the local perception of individuals for movement, while in the other two it is taken into account that they have a sharper sensory capacity and also analyze conditions at nearby sites. Several discrete model simulations were performed for several parameter sets and the continuous formulations corresponding to each one of the models were obtained. The resulting spatial patterns were classified as homogeneous, stable heterogeneous, oscillatory heterogeneous or unstable. Thus, we conclude that the three proposed models can represent aggregation mechanisms and that this process occurred more effectively considering that individuals can perceive not only the density at their site, but also at neighboring sites. |
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2020-03-06T19:57:21Z2020-03-06T19:57:21Z2019-12-12http://repositorio.ufsm.br/handle/1/19763The mechanisms that can lead to the formation of heterogeneous distribution of individuals of many biological species arouse the interest of researchers from various areas. Many mathematical models of pattern formation are based on the Turing mechanism and on aggregation processes in relation to concentration gradients of a chemical substance. Recently, the Cahn-Hilliard principle of phase separation, which assumes density-dependent movement, has been used to study self-organized mussel patterns. In this work, we formulate three discrete models of coupled map networks with density-dependent movement to describe processes of aggregation and formation of spatial patterns. Some species show better development at intermediate densities, avoiding problems related to overpopulation or the difficulty of keeping the species at low population densities. Thus, the first model considers only the local perception of individuals for movement, while in the other two it is taken into account that they have a sharper sensory capacity and also analyze conditions at nearby sites. Several discrete model simulations were performed for several parameter sets and the continuous formulations corresponding to each one of the models were obtained. The resulting spatial patterns were classified as homogeneous, stable heterogeneous, oscillatory heterogeneous or unstable. Thus, we conclude that the three proposed models can represent aggregation mechanisms and that this process occurred more effectively considering that individuals can perceive not only the density at their site, but also at neighboring sites.Os mecanismos que podem levar à formação de distribuição heterogênea de indivíduos de muitas espécies biológicas despertam o interesse de pesquisadores de diversas áreas. Muitos modelos matemáticos de formação de padrões são baseados no mecanismo de Turing e em processos de agregação em relação a gradientes de concentração de uma substância química. Recentemente, o princípio de Cahn-Hilliard de separação de fase, que supõe movimentação dependente da densidade, foi usado para estudar os padrões auto-organizados de mexilhões. Neste trabalho, formulamos três modelos discretos de redes de mapas acoplados com movimentação dependente da densidade para descrever processos de agregação e formação de padrões espaciais. Algumas espécies apresentam melhor desenvolvimento em densidades intermediárias, evitando problemas relacionados à superpopulação ou à dificuldade de manter a espécie em baixas densidades populacionais. Assim, o primeiro modelo considera apenas a percepção local dos indivíduos para a movimentação, enquanto nos outros dois é levado em conta que eles possuem uma capacidade sensorial mais aguçada e analisam também as condições em sítios próximos. Foram realizadas diversas simulações dos modelos discretos para vários conjuntos de parâmetros e foram obtidas as formulações contínuas correspondentes a cada um dos modelos. Os padrões espaciais resultantes foram classificados como homogêneos, heterogêneos estáveis, heterogêneos oscilatórios ou instáveis. Dessa forma, concluímos que os três modelos propostos conseguem representar mecanismos de agregação e que esse processo ocorreu de maneira mais eficaz ao considerar que os indivíduos conseguem perceber não só a densidade no sítio em que se encontram, mas também nos sítios vizinhos.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESporUniversidade Federal de Santa MariaCentro de Ciências Naturais e ExatasPrograma de Pós-Graduação em MatemáticaUFSMBrasilMatemáticaAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAgregaçãoFormação de padrões espaciaisMovimentação dependente da densidadeRedes de mapas acopladosAggregationSpatial pattern formationDensity-dependent movementCoupled map networksCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAModelos discretos para agregação populacionalDiscrete models for population aggregationinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisRodrigues, Luiz Alberto Díazhttp://lattes.cnpq.br/9198489380493317Meyer, João Frederico da Costa Azevedohttp://lattes.cnpq.br/9611168473482242Emmendorfer, Leonardo Ramoshttp://lattes.cnpq.br/1129100746134234http://lattes.cnpq.br/9638073533973400Rossato, Marcelo Cargnelutti100100000008600d9779333-92f7-4d34-94b4-18f90b2d4fd4736c91e2-8183-49e4-937e-dc35a415c5122d5c8d8e-8776-42b5-b84c-e59cef95a69c1ba56e4b-7b99-499b-86c4-b040c485da00reponame:Repositório Institucional Manancial UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMORIGINALDIS_PPGMATEMATICA__2019_ROSSATO_MARCELO.pdfDIS_PPGMATEMATICA__2019_ROSSATO_MARCELO.pdfDissertação de Mestradoapplication/pdf9314620http://repositorio.ufsm.br/bitstream/1/19763/1/DIS_PPGMATEMATICA__2019_ROSSATO_MARCELO.pdf327ec5bddd395386a99e433cd11870c2MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.por.fl_str_mv |
Modelos discretos para agregação populacional |
dc.title.alternative.eng.fl_str_mv |
Discrete models for population aggregation |
title |
Modelos discretos para agregação populacional |
spellingShingle |
Modelos discretos para agregação populacional Rossato, Marcelo Cargnelutti Agregação Formação de padrões espaciais Movimentação dependente da densidade Redes de mapas acoplados Aggregation Spatial pattern formation Density-dependent movement Coupled map networks CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Modelos discretos para agregação populacional |
title_full |
Modelos discretos para agregação populacional |
title_fullStr |
Modelos discretos para agregação populacional |
title_full_unstemmed |
Modelos discretos para agregação populacional |
title_sort |
Modelos discretos para agregação populacional |
author |
Rossato, Marcelo Cargnelutti |
author_facet |
Rossato, Marcelo Cargnelutti |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Rodrigues, Luiz Alberto Díaz |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/9198489380493317 |
dc.contributor.referee1.fl_str_mv |
Meyer, João Frederico da Costa Azevedo |
dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/9611168473482242 |
dc.contributor.referee2.fl_str_mv |
Emmendorfer, Leonardo Ramos |
dc.contributor.referee2Lattes.fl_str_mv |
http://lattes.cnpq.br/1129100746134234 |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/9638073533973400 |
dc.contributor.author.fl_str_mv |
Rossato, Marcelo Cargnelutti |
contributor_str_mv |
Rodrigues, Luiz Alberto Díaz Meyer, João Frederico da Costa Azevedo Emmendorfer, Leonardo Ramos |
dc.subject.por.fl_str_mv |
Agregação Formação de padrões espaciais Movimentação dependente da densidade Redes de mapas acoplados |
topic |
Agregação Formação de padrões espaciais Movimentação dependente da densidade Redes de mapas acoplados Aggregation Spatial pattern formation Density-dependent movement Coupled map networks CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Aggregation Spatial pattern formation Density-dependent movement Coupled map networks |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
The mechanisms that can lead to the formation of heterogeneous distribution of individuals of many biological species arouse the interest of researchers from various areas. Many mathematical models of pattern formation are based on the Turing mechanism and on aggregation processes in relation to concentration gradients of a chemical substance. Recently, the Cahn-Hilliard principle of phase separation, which assumes density-dependent movement, has been used to study self-organized mussel patterns. In this work, we formulate three discrete models of coupled map networks with density-dependent movement to describe processes of aggregation and formation of spatial patterns. Some species show better development at intermediate densities, avoiding problems related to overpopulation or the difficulty of keeping the species at low population densities. Thus, the first model considers only the local perception of individuals for movement, while in the other two it is taken into account that they have a sharper sensory capacity and also analyze conditions at nearby sites. Several discrete model simulations were performed for several parameter sets and the continuous formulations corresponding to each one of the models were obtained. The resulting spatial patterns were classified as homogeneous, stable heterogeneous, oscillatory heterogeneous or unstable. Thus, we conclude that the three proposed models can represent aggregation mechanisms and that this process occurred more effectively considering that individuals can perceive not only the density at their site, but also at neighboring sites. |
publishDate |
2019 |
dc.date.issued.fl_str_mv |
2019-12-12 |
dc.date.accessioned.fl_str_mv |
2020-03-06T19:57:21Z |
dc.date.available.fl_str_mv |
2020-03-06T19:57:21Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://repositorio.ufsm.br/handle/1/19763 |
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http://repositorio.ufsm.br/handle/1/19763 |
dc.language.iso.fl_str_mv |
por |
language |
por |
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100100000008 |
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600 |
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Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Centro de Ciências Naturais e Exatas |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Matemática |
dc.publisher.initials.fl_str_mv |
UFSM |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Matemática |
publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Centro de Ciências Naturais e Exatas |
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