Motions under focal attraction in planar vector fields
In this work, we develop the article ?On the motion under focal attractionin a rotating medium?, of J. Sotomayor, which deals with a bidimensionaldifferential system that model the following Biological problem: in a shallowrecipient with circular section, with liquid in, spinning with angular speed amp;#969;, thereare platyhelminthes, flatworms organisms, they are attracted by a fix lightingpoint near of the border of the recipient and they swim with a speed v in thedirection of the this point. The problem is to show that there exists an equilibriumpoint where platyhelminthes go to cluster by the time passing. It?s analyzed thedynamic of the model: existence of critical points and stability of the system andbifurcations. We analyzed three modifications of this system too. In the lastpart, it?s discussed a criterium for non existence of periodic orbits of a planarvector fields in a simply connected region.
Advisor:Ronaldo Alves Garcia
School:Universidade Federal de Goiás
Source Type:Master's Thesis
Keywords:Fold, Pitchfork and Bogdanov-Takens bifurcations
Date of Publication:08/29/2008