Bifurcation of equilibrium points

The number of equilibria of the differential equations depend on the parameter a. Variyng the value of the parameter, the constant solutions and a solution such that y(0)=1 are shown. A bifurcation occurs when the number of equilibria (constant solutions) change. Move the slider to see when the bifurcation occurs.
How many equilibria there exist depending on the parameter? Can you predict the limit of y(t) as t tends to infinity depending on the value of y(0)?