A nonlinear circuit model with periodic switching is established. The fold bifurcation and Hopf bifurcation sets of the subsystems are derived via the analysis of the relevant equilibrium points as well as the stabilities. Complex dynamical behaviors caused by periodic switching in various equilibrium states of subsystems are investigated. The results show that there exist two types of destabilizing cases, i.e., period-doubling bifurcation and saddle-node bifurcation, in the variation of periodic solution to the switching system with parameter, leading to different forms of chaotic oscillations correspondingly. Furthermore, by analyzing the the phase trajectory and its corresponding bifurcation, the mechanisms for different types of oscillations are presented, which can explain some phenomena of the switched dynamical system.