  In this paper, several results concerning attraction and asymptotic stability
in the large of nonlinear ordinary differential equations are presented. The
main result is very simple to apply yielding a sufficient condition under which
the equilibrium point (assuming a unique equilibrium) is attractive and also
provides a variety of options among them the classical linearization and other
existing results are special cases of the this main theorem in this paper
including and extension of the well known Markus-Yamabe conjecture. Several
application examples are presented in order to analyze the advantages and
drawbacks of the proposed result and to compare such results with successful
existing techniques for analysis available in the literature nowadays.
