Resumo:
Nodes are equilibria of a planar differential equation or vector field whose eigenvalues
have the same sign. Star nodes are nodes whose eigenvalues are equal and nonzero. Limit
cycles are closed and isolated orbits in the set of closed orbits of a vector field. This work
aims to find conditions, as general as possible, in order to guarantee the coexistence of
limit cycles and star nodes. Such a study is done in a convenient way: take a family of
differential equations whose origin is a star node equilibrium and searches for conditions
for the existence of a limit cycle around the origin. Later, the study is generalized and
some results contemplate other types of equilibria.
