On a model for the temporal oscillations in the Belousov-Zhabotinsky reaction

The detailed chemical mechanism for the temporal oscillations in the Belousov-Zhabotinsky reaction, which was suggested by Field, Körös, and Noyes J. Am. Chem. Soc. 94, 8649 (1972), has been reconsidered by Field and Noyes J. Chem. Phys. 60, 1877(1974), who suggest a simplified five step scheme to explain the chemical behavior that is observed. Their reaction equations are discussed here, and a method for finding bounds for closed stable trajectories in the phase space of the dimensionless concentrations of the HBrO2, Br−, and Ce(IV) is given. Simple bounds are obtained and compared with the numerical solution found by Field and Noyes. The existence of such bounds proves that the equations suggested by Field and Noyes are globally stable for large enough disturbances from the steady state and provide necessary conditions for the existence of bounded temporal oscillations.