Planar regions of attraction

An effective method for estimation of the region of attraction of an equilibrium point in the plane is proposed in this note. This new method for stability analysis of the second-order nonlinear system
\dot{x} = f(x)
;
x(t_{0})=x_{0}
, is based on the properties of phase flows and associated velocity fields. Several engineering examples have been solved which illustrate the usefulness of the technique.