On the synchronizing mechanism of a class of cellular automata

We analyze the onset of local oscillations in a class of cellular automata introduced by Vieira and Bisch (1993). They consist in one autocatalytic reaction and a ring of spontaneously decaying processes. We explain, in the context of recent studies on synchronization of generalized Forest-Fire models, why a minimum number of chemical species is needed for oscillations to take place. Numerical simulations confirm our analysis.