The regular behavior of the Cepheids has been successfully modeled with numerical hydrodynamics since the 1960s, and from a theoretical point of view it is easily understood as due to the presence of center manifold which arises because of the weakly dissipative nature of the dynamical system. This, and the fact that the pulsations are weakly nonlinear, allows a description of the system in terms of amplitude equations and a construction of the bifurcation diagram (see also bifurcation theory) of the possible types of pulsation (or limit cycles), such fundamental mode pulsation, first or second overtone pulsation, or more complicated, double-mode pulsations in which several modes are excited with constant amplitudes. The boundaries of the instability strip where pulsation sets in during the star's evolution correspond to a Hopf bifurcation.