Estudo de um modelo de movimento sob atração focal num fluido raso com rotação: análise qualitativa

Abstract

This work has its initial motivation in the article “On the motion under focal attraction in a rotating medium”, by J. Sotomayor [9], which models the following problem of planar differential equations present, for example, in biology: Inside a shallow circular container, we put a liquid and several species of flatworms that swim with different speeds in the direction of a luminous point fixed on the edge of this container. The objective is to subject the liquid to a constant rotation in order to isolate each of the different species present in the experiment. After this initial study, two modifications were made in the model of differential equations, adding a radial drift to the system. Through these modifications, we studied the bifurcation diagram of each of these systems, which involved bifurcations of Bogdanov-Takens, Hopf and Saddle-node types.