DS Quadratic

f(x)= x^2 + b x + c

When b=0, this is the famous quadratic mapping of the real interval. (See R. Devaney, An Introduction to Chaotic Dynamical Systems, Benjamin-Cummings, 1986.

The set of points for which f(x)-x=0 are the fixed points for this mapping. The set of points for which f(x)-x = f'(x)-1 = 0 are called points of saddle-node bifurcation.

Since this model has a one-dimensional domain, one or more of the parameters must be permuted into the domain before attempting to trace level sets.