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Master's Dissertation
DOI
10.11606/D.45.2010.tde-18082010-122313
Document
Author
Full name
Andre Ricardo Belotto da Silva
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2010
Supervisor
Committee
Tello, Jorge Manuel Sotomayor (President)
Garcia, Ronaldo Alves
Salomão, Pedro Antonio Santoro
Title in Portuguese
Análise das bifurcações de um sistema de dinâmica de populações
Keywords in Portuguese
Bifurcação
Bogdanov-Takens
Bogdanov-Takens degenerado
Centros organizadores
Elíptica-nilpotente
Foco-nilpotente
Função resposta Holling IV
Hopf
Lotka-Volterra
Predador-presa
Abstract in Portuguese
Nesta dissertação, tratamos do estudo das bifurcações de um modelo bi-dimensional de presa-predador, que estende e aperfeiçoa o sistema de Lotka-Volterra. Tal modelo apresenta cinco parâmetros e uma função resposta não monotônica do tipo Holling IV: $$ \left\{\begin \dot=x(1-\lambda x-\frac{\alpha x^2+\beta x +1})\\ \dot=y(-\delta-\mu y+\frac{\alpha x^2+\beta x +1}) \end ight. $$ Estudamos as bifurcações do tipo sela-nó, Hopf, transcrítica, Bogdanov-Takens e Bogdanov-Takens degenerada. O método dos centros organizadores é usado para estudar o comportamento qualitativo do diagrama de bifurcação.
Title in English
Bifurcation analysis of a system for population dynamics
Keywords in English
Bifurcation
Bogdanov-Takens
Degenerate Bogdanov-Takens
Holling IV response funciton
Hopf
Lotka-Volterra
Nilpotent eliptic
Nilpotent focus
Organising centers
Predator-prey
Abstract in English
In this work are studied the bifurcations of a bi-dimensional predator-prey model, which extends and improves the Volterra-Lotka system. This model has five parameters and a non-monotonic response function of Holling IV type: $$ \left\{\begin \dot=x(1-\lambda x-\frac{\alpha x^2+\beta x +1})\\ \dot=y(-\delta-\mu y+\frac{\alpha x^2+\beta x +1}) \end ight. $$ They studied the sadle-node, Hopf, transcritic, Bogdanov-Takens and degenerate Bogdanov-Takens bifurcations. The method of organising centers is used to study the qualitative behavior of the bifurcation diagram.
 
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Publishing Date
2011-05-12
 
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