# Bifurcation Diagram and Determining Stability of Equilibria

I just have a question regarding equilibrium points and bifurcation diagrams. This is the question that we are being asked;

For the following models, which contain a parameter $$h$$, find the equilibria in terms of $$h$$ and determine their stability. Construct a bifurcation diagram showing how the equilibria depend upon $$h$$. and label the branches of the curves in the diagram as stable or unstable. $$1.\space\space\space\space u'=hu-u^2$$ $$2.\space\space\space\space u'=(1-u)(u^2-h)$$

I have determined the equilibrium solutions in terms of $$h$$. For 1. $$h=u$$ and for 2. $$h=u^2$$

When determining their stability do we assume that $$h$$ is just some constant and determine the second derivative with respect to $$h$$ and continue by substituting our equilibrium value in? Or is there something else that we need to do.

I have done a bit of searching for bifurcation diagrams but I have not found any way that I can plot it with the materials available. By any chance is there some program that I could use to display this on a diagram?

Any help would be greatly appreciated! Thanks in advance.