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Master's Dissertation
DOI
10.11606/D.100.2017.tde-01062017-120551
Document
Author
Full name
Sergio Serino
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2016
Supervisor
Committee
Mendonca, Jose Ricardo Goncalves de (President)
Almeida, Ariovaldo José de
Bevilacqua, Joyce da Silva
Ramos, Alexandre Ferreira
Title in Portuguese
Dinâmica e estabilidade em um modelo para populações de ostras
Keywords in Portuguese
Critérios de Routh-Hurwitz
Dinâmica de populações
Método de Quirk-Ruppert
Sistemas complexos
Sistemas dinâmicos
Abstract in Portuguese
O objetivo deste trabalho é estudar a ocorrência de mudanças de regime típicas de comportamentos em sistemas complexos, em particular no contexto de sistemas dinâmicos aplicados. Para isso, desenvolvemos um modelo matemático que representa a interação entre uma cultura de ostras utilizadas para consumo humano e os processos de eutrofização e biorremediação do ecossistema que as contém. As interações entre as populações de ostras e do fitoplâncton entre si e com a matéria suspensa, subproduto das relações entre os componentes do meio e seu processo de eutrofização, alteram os níveis de oxigenação e a consequente qualidade da ´agua devido `a realização de maior ou menor quantidade de fotossíntese pelas vegetações mais profundas do meio. Neste trabalho propomos um sistema dinâmico de três variáveis para modelar esse sistema e analisamos seus pontos de equilíbrio usando duas técnicas, método de Quirk-Ruppert e os critérios de Routh-Hurwitz, além de resolvê-lo numericamente para um conjunto de parâmetros realísticos (fenomenológicos) obtidos a partir da literatura especializada. Nossos resultados indicam que o limite de extração diária de ostras que pode ser realizado sem levar a cultura ao colapso gira em torno de 4.8% da população
Title in English
Dynamics and stability in a model for oyster populations
Keywords in English
Complex systems
Dynamical systems
Method of Quirk-Ruppert
Population dinamics
Routh-Hurwits criteria
Abstract in English
The objective of this work is to study the occurrence of regime shifts that are typical in the behavior of complex systems, in particular in the context of applied dynamical systems. Accordingly, we have developed a mathematical model that represents the interaction between a culture of oysters used for human consumption and the eutrophication and bioremediation processes of the ecosystem containing the culture. The interactions between the oyster populations and the phytoplankton between themselves and with the suspended matter, that appears as a by-product of the relationship between the components of the medium and its eutrophication process, change the oxygenation levels and the resulting water quality due to the realization of a greater or lesser amount of photosynthesis by the vegetation of the deeper levels. In this paper we propose a dynamical system of three variables to model the system and analyze its points of equilibrium using two techniques, the Quirk-Ruppert method and the Routh-Hurwitz criteria, besides solving the equations numerically for a realistic phenomenological) set of parameters obtained from the literature. Our results indicate that the daily extraction threshold that can be achieved without collapsing the culture of oysters amounts to approximately 4.8% of the total population
 
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Publishing Date
2017-06-14
 
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