There are two steady states,
, shown by the green and red points.
Restricting the parameters to
, we compute and plot the region of asymptotic stability, shown in orange. All trajectories originating at an initial condition (IC) chosen in this orange region end at the
. Trajectories diverge otherwise. The blue region is also a basin of attraction for
. This region is obtained using Lyapunov's direct method and the Lyapunov function
. The blue region cannot contain
because it is an unstable steady state.
defines a closed curve containing the origin if
is a positive constant. The largest such region can be obtained by having
at its frontier, or
. You can drag the locator to change the IC.