Applying the regression analysis to the measured data in CO oxidation on platinum group metals, a analytical theory model with different time scales is established in this paper. The stabilities of equilibria are discussed in detail, and different types of the solutions may bifurcate from the equilibria with the change of the parameters. With a certain parameter, the system can exhibit periodic oscillations via the saddle-node homoclinic orbit bifurcation, which can evolve into periodic bursting, owing to Hopf bifurcation of the fast subsystem. The bifurcation connecting the quiescent state and the repetitive spikes is presented to account for the occurrence of the Nk oscillations. Furthermore, the mechanism of sequence of the period-adding bifurcations is explored to reveal why the length of the sequences become longer with the variation of the parameters.