A tutorial introduction to bifurcation theory and the applicability of this theory in studying nonlinear dynamical phenomena in a power system network is explored. Systematic application of the theory revealed the existence of stable and unstable periodic solutions as well as voltage collapse. A particular response depends on the value of the parameter under consideration. It has been shown that voltage collapse is a subset of overall bifurcation phenomena a system may experience under the influence of system parameters. A low-dimensional center manifold reduction is applied to capture the relevant dynamics involved in the voltage collapse process. The study also emphasizes the need for the consideration of nonlinearity, especially when the system is highly stressed.<<ETX>>