A mathematical model for bifurcations in a Belousov–Zhabotinsky reaction

In our investigation we find that there are three stages during the whole lifespan of a Belousov–Zhabotinsky (BZ) system with 1,4-cyclohexanedione (CHD) and ferroin: transitional period (TP), induction period (IP), and main period (MP). When the system goes from the TP to the IP, there is a bifurcation from monostability (orange steady-state) to bistability (both orange and blue steady-states). When the system shifts from the IP to the MP, a different bifurcation occurs from the bistability back to the monostability (orange steady-state). A reduction step before the second bifurcation propagates slower than oxidation steps and pulses during the whole lifespan of the medium. This sharp difference of propagation speed has not been observed in other BZ systems, and cannot be interpreted by the prototype Oregonator model. We construct here an Oregonator-type model that simulates the two bifurcations and the propagation speed difference of the two kinds of step before the second bifurcation. Furthermore, our model demonstrates other bifurcations that are not observable in experiment. Our discovery not only unfolds a new aspect of the well-studied BZ reaction, but also leads to a new demand for further understanding of a reaction–diffusion equation system as the corresponding ordinary differential equation system bifurcates.