A mathematical model of the Bray–Liebhafsky reaction

It is known that the widely studied Bray–Liebhafsky reaction typically exhibits complex chemical behaviour. Numerous mathematical systems have been proposed to describe the iodine oscillations that occur during this process. Recently, a four-variable model of the Bray–Liebhafsky reaction has been proposed and analytical and numerical investigations suggested that chaotic solutions may exist. We revisit this four-variable model here and perform what appears to be the first detailed work on this system. We suggest that this model is perhaps not chaotic after all. Informed by these fresh insights, we propose a reduced two-variable model based upon the four-variable system. This model is created with the twin goals of enabling simpler mathematical analysis while retaining the underlying chemical mechanisms. We are able to demonstrate that our reduced problem performs very well when compared with the full model for realistic parameter values. In particular, key regions of parameter space are identified within which temporal oscillations can occur. Moreover, these persistent oscillations are consistent with the available qualitative experimental observations.