How to plot bifurcation diagram?

Hi to everyone, I have a system of 16 non linear equations that come from PDEs at steady state. I have used fsolve to find equilibrium points and I change randomly initial conditions so that I run the program a lot of times obtaining all the possibile solutions. Now, the problem is that I want to obtain a bifurcation plot varying a parameter that is in my system. How can I do that? How can I understand if an equilibrium point is stable or not?