KCC-theory and its applications to coral reef modelling
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/54849 |
Resumo: | The systems of second order differential equations (SODE) have played a very important role in the study of physics and biological models, in particular, the Volterra-Hamilton system is one of the most useful SODE in ecological problems. We develop the required background of Finsler geometry and classical equation of ecological models to study some aspects of the tra- jectories of a Volterra-Hamilton system and other subject called semispray. Some geometrical invariants, called KCC-invariants, there are five, are computed to study aspects of the solution trajectories of a semispray. We use Volterra-Hamilton systems theory and their associated cost functional to study the population dynamics and productive processes of coral reefs together with their symbiont algae in recovery from bleaching and show that the cost of production remains the same after the process. The KCC-theory geometrical invariants are determined for the model proposed to describe the renewed symbiotic interaction between coral and algae. |
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CAVALCANTI, Rafael dos Santoshttp://lattes.cnpq.br/5474431234208461http://lattes.cnpq.br/9476240387217710http://lattes.cnpq.br/9796606313634647RUTZ, Solange da FonsecaANTONELLI, Peter Louis2024-01-29T14:33:12Z2024-01-29T14:33:12Z2022-05-26CAVALCANTI, Rafael dos Santos. KCC-theory and its applications to coral reef modelling. 2022. Dissertação (Mestrado em Matemática) – Universidade Federal de Pernambuco, Recife, 2022.https://repositorio.ufpe.br/handle/123456789/54849The systems of second order differential equations (SODE) have played a very important role in the study of physics and biological models, in particular, the Volterra-Hamilton system is one of the most useful SODE in ecological problems. We develop the required background of Finsler geometry and classical equation of ecological models to study some aspects of the tra- jectories of a Volterra-Hamilton system and other subject called semispray. Some geometrical invariants, called KCC-invariants, there are five, are computed to study aspects of the solution trajectories of a semispray. We use Volterra-Hamilton systems theory and their associated cost functional to study the population dynamics and productive processes of coral reefs together with their symbiont algae in recovery from bleaching and show that the cost of production remains the same after the process. The KCC-theory geometrical invariants are determined for the model proposed to describe the renewed symbiotic interaction between coral and algae.CNPqAs equações diferenciais de segunda ordem (SODE) têm desempenhado um importan- tissímo papel do estudo de modelos físicos e biológicos, em particular, o sistema de Volterra- Hamilton é um dos SODE mais usados em problemas ecológicos. Desenvolvemos os assuntos necessários de geometria Finsler e quações clássicas de modelos ecológicos afim de esturdar- mos alguns aspectos das trajetórias que são soluções de um sistema de Volterra-Hamilton e outro objeto chamado de semispray. Alguns invariantes geométricos, chamados de invariantes KCC, são cinco, são calculados para estudar aspectos das trajetótias soluções de um semispray. Usamos a teoria dos sistemas de Volterra-Hamilton e seus funcionais de custo para estudar a dinamica populacional e o processo de produção de um recife de cora, junto com suas algas simbióticas, em recuperação de branqueamento, mostrar que o custo de produção permanece o mesmo após o processo. A teoria KCC com seus invariantes geométricos são determinantes para o modelo proposto afim de descrever a interação simbiótica renovada entre as algas e os corais.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em MatematicaUFPEBrasilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessGeometriaTeoria KCCKCC-theory and its applications to coral reef modellinginfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesismestradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPELICENSElicense.txtlicense.txttext/plain; charset=utf-82362https://repositorio.ufpe.br/bitstream/123456789/54849/3/license.txt5e89a1613ddc8510c6576f4b23a78973MD53CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufpe.br/bitstream/123456789/54849/2/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD52ORIGINALDISSERTAÇÃO Rafael dos Santos Cavalcanti.pdfDISSERTAÇÃO Rafael 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dc.title.pt_BR.fl_str_mv |
KCC-theory and its applications to coral reef modelling |
title |
KCC-theory and its applications to coral reef modelling |
spellingShingle |
KCC-theory and its applications to coral reef modelling CAVALCANTI, Rafael dos Santos Geometria Teoria KCC |
title_short |
KCC-theory and its applications to coral reef modelling |
title_full |
KCC-theory and its applications to coral reef modelling |
title_fullStr |
KCC-theory and its applications to coral reef modelling |
title_full_unstemmed |
KCC-theory and its applications to coral reef modelling |
title_sort |
KCC-theory and its applications to coral reef modelling |
author |
CAVALCANTI, Rafael dos Santos |
author_facet |
CAVALCANTI, Rafael dos Santos |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/5474431234208461 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/9476240387217710 |
dc.contributor.advisor-coLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/9796606313634647 |
dc.contributor.author.fl_str_mv |
CAVALCANTI, Rafael dos Santos |
dc.contributor.advisor1.fl_str_mv |
RUTZ, Solange da Fonseca |
dc.contributor.advisor-co1.fl_str_mv |
ANTONELLI, Peter Louis |
contributor_str_mv |
RUTZ, Solange da Fonseca ANTONELLI, Peter Louis |
dc.subject.por.fl_str_mv |
Geometria Teoria KCC |
topic |
Geometria Teoria KCC |
description |
The systems of second order differential equations (SODE) have played a very important role in the study of physics and biological models, in particular, the Volterra-Hamilton system is one of the most useful SODE in ecological problems. We develop the required background of Finsler geometry and classical equation of ecological models to study some aspects of the tra- jectories of a Volterra-Hamilton system and other subject called semispray. Some geometrical invariants, called KCC-invariants, there are five, are computed to study aspects of the solution trajectories of a semispray. We use Volterra-Hamilton systems theory and their associated cost functional to study the population dynamics and productive processes of coral reefs together with their symbiont algae in recovery from bleaching and show that the cost of production remains the same after the process. The KCC-theory geometrical invariants are determined for the model proposed to describe the renewed symbiotic interaction between coral and algae. |
publishDate |
2022 |
dc.date.issued.fl_str_mv |
2022-05-26 |
dc.date.accessioned.fl_str_mv |
2024-01-29T14:33:12Z |
dc.date.available.fl_str_mv |
2024-01-29T14:33:12Z |
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.citation.fl_str_mv |
CAVALCANTI, Rafael dos Santos. KCC-theory and its applications to coral reef modelling. 2022. Dissertação (Mestrado em Matemática) – Universidade Federal de Pernambuco, Recife, 2022. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/54849 |
identifier_str_mv |
CAVALCANTI, Rafael dos Santos. KCC-theory and its applications to coral reef modelling. 2022. Dissertação (Mestrado em Matemática) – Universidade Federal de Pernambuco, Recife, 2022. |
url |
https://repositorio.ufpe.br/handle/123456789/54849 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Matematica |
dc.publisher.initials.fl_str_mv |
UFPE |
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Brasil |
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Universidade Federal de Pernambuco |
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