Based on a power-factor-correction (PFC) boost converter, a class of nonlinear phenomena are described when the system switches between saturated and non-saturated states alternately. Their characteristics and origination are analyzed. According the piecewise differential equations derived, we simulate the system's dynamical behavior. The simulating results demonstrate that period-doubling bifurcation and chaos may occur in this system. Moreover, border-collision bifurcation and transition from chaos to period-1 may also appear. These nonlinear phenomena result from the abrupt change of the system's qualitative behavior when the rectified input current runs into its saturation border. The nonlinear phenomena caused by saturation and the related analysis are verified by the experimental results.