Movimentos sob atração focal em campos vetoriais planares / Motions under focal attraction in planar vector fields

AUTOR(ES)

Tiberio Bittencourt de Oliveira Martins

DATA DE PUBLICAÇÃO

2008

RESUMO

In this work, we develop the article On the motion under focal attraction in a rotating medium, of J. Sotomayor, which deals with a bidimensional differential system that model the following Biological problem: in a shallow recipient with circular section, with liquid in, spinning with angular speed ω, there are platyhelminthes, flatworms organisms, they are attracted by a fix lighting point near of the border of the recipient and they swim with a speed v in the direction of the this point. The problem is to show that there exists an equilibrium point where platyhelminthes go to cluster by the time passing. Its analyzed the dynamic of the model: existence of critical points and stability of the system and bifurcations. We analyzed three modifications of this system too. In the last part, its discussed a criterium for non existence of periodic orbits of a planar vector fields in a simply connected region.

ASSUNTO(S)

equações diferenciais bidimencionais matematica campos vetoriais planares biologia; equações diferenciais bidimencionais; dinâmica de modelagem platelmintos campos vetoriais planares biologia dinâmica de modelagem platelmintos fold, pitchfork and bogdanov-takens bifurcations

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