Bifurcation: dy/dt = y^2 + a

This animation shows the bifurcation of the one-parameter family of ODEs described by dy/dt = y^2 + a. Increasing the parameter a from negative to positive shifts the graph of the parabola vertically effectively changing the number of equilibrium solutions from two, for a less than zero, to one, for a equal to zero, and finally to none, for a greater than zero. This means a bifurcation occurs at a = 0, which is demonstrated in the animation. Also, the slope field is presented as well as a trace of the bifurcation diagram.