By introducing weakly periodic perturbation given by light,the three-variable model of photosensitive BelousovZhabotinsky reaction with two time scales may possess two slow processes.The codimension-2 bursting called cusp bursting is novel,especially the phenomenon that is of the transiently quiescent state mixed among repetitively large amplitude oscillations.The slow-fast dynamics analysis with two slow parameters,based on overlapping the codimension-2 bifurcation diagram of the fast subsystem with the 3-dimensional transition phase portrait of the whole system,is proposed to reveal the bifurcation mechanism of bursting oscillation with two slow variables.The adjustment behavior of slow parameters is used to explain the transformation between the spiking state and quiescent state.