In this chapter, we will discuss how the dynamical evolution—and thus the convergence to theFixed point fixed point—-takes place. We will consider an investigation both at the bifurcation and in its vicinity. We will show that, at the bifurcation, the decay toward the fixed point is described by aGeneralized homogeneous functiongeneralized homogeneous function with threeCritical exponents critical exponents: \(\alpha \) , \(\beta \) , and z. Near the bifurcation, the decay to the fixed point is exponential, with a relaxation time described by a power law measured with respect to the distance from the control parameter to the bifurcation point, with exponent \(\delta \) . These four critical exponents define theUniversality class universality class to which the bifurcation belongs.