Single-Hopf Bursting in Periodic Perturbed Belousov–Zhabotinsky Reaction with Two Time Scales

By introducing weak periodic perturbation to the Oregonator, we investigate a mathematical model with two time scales. The novel dynamical phenomena called the single-Hopf bursting with unusually quiescent state are observed. The related bifurcation mechanism is presented by means of the transition portrait and slow-fast analysis, which has rarely been reported in the previous works associated with the Oregonator model. Furthermore, the influence of forcing amplitude on bursting behaviors is studied. Further investigation finds that excitation amplitude may play an important role in a two-timescale system with the slow procedure dominated by periodic perturbation.