What are the bifurcation values for the equation:
dy/dt = y^3 +ay^2
The Attempt at a Solution
y^3 + ay^2 = 0
==> y^2 (y + a) = 0
==> y = 0 (double root), or y = -a.
a = 0 is the sole bifurcation point, since
a < 0 ==> two equilibrium solutions
a = 0 ==> one equilibrium solution
a > 0 ==> two equilibrium solutions.
my question is how can you tell that a < 0 has two equilibrium solutions and a=0 has one and a>0 has two again?