Bifurcation of invariant manifolds in smooth and non-smooth differential systems
Bifurcations of nested invariant tori and invariant sets of Lotka-Volterra differe...
The Center-Focus problem, Abelian integrals and the Hilbert's 16th problem
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Author(s): |
Andre Ricardo Belotto da Silva
Total Authors: 1
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Document type: | Master's Dissertation |
Press: | São Paulo. |
Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
Defense date: | 2010-07-16 |
Examining board members: |
Jorge Manuel Sotomayor Tello;
Ronaldo Alves Garcia;
Pedro Antonio Santoro Salomão
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Advisor: | Jorge Manuel Sotomayor Tello |
Abstract | |
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. (AU) |