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Bifurcation analysis of a system for population dynamics

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Author(s):
Andre Ricardo Belotto da Silva
Total Authors: 1
Document type: Master's Dissertation
Press: São Paulo.
Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
Defense date:
Examining board members:
Jorge Manuel Sotomayor Tello; Ronaldo Alves Garcia; Pedro Antonio Santoro Salomão
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)