I have a 6d system of dynamic equations. I am able to calculate numerically the steady states and evaluate their local stability. It turns out that everything depends on one parameter, call it C. If it is smaller than 0, there are no real solutions. If it is larger than 0, there are two solutions, one stable and one unstable. It seems that there is a saddle-node type of bifurcation. But the problem is that for C=0 the system is undefined, i.e. there is a division by C.
Can I say that there is a bifurcation at point C even if the function is undefined at this point? Is it then a saddle-node bifurcation? I read that C=0 is the singular point but how does it relate to the bifurcation theory? How should I treat this point? Do you have any ideas? Thanks!