Using the fixed point x=0 and
x=0 is a atracting fixed point , cause .
for the other fixed point
evaluating , you get
in case you want to know the values for so that is an atracting fixed point you have to solve the inequality
and for a repelling fixed point solve:
to sketch the bifurcation, in the x -axis you plot and in the y-axis put the fixed points.
locate the coordinates , and the use the results of the inequalities to draw the behaviour your are looking for.!