Multi-state stochastic hotchpotch model gives rise to the observed mesoscopic behaviour in the non-stirred Belousov--Zhabotinsky reaction

Mesoscopic dynamics of self-organized structures is the most important aspect in the description of complex living systems. The Belousov--Zhabotinsky (B--Z) reaction is in this respect a convenient testbed because it represents a prototype of chemical self-organization with a rich variety of emergent wave-spiral patterns. Using a multi-state stochastic hotchpotch model, we show here that the mesoscopic behaviour of the non-stirred B--Z reaction is both qualitatively and quantitatively susceptible to the description in terms of stochastic multilevel cellular automata. This further implies that the mesoscopic dynamics of the non-stirred B--Z reaction results from a delicate interplay between a) a maximal number of available states within the elementary time lag (i.e. a minimal time interval needed for demise of a final state) and b) an imprecision or uncertainty in the definition of state. If either the number of time lags is largely different from 7 or the maximal number of available states is smaller than 20, the physicochemical conditions are inappropriate for a formation of the wave-spiral patterns. Furthermore, a white noise seems to be key for the formation of circular structures (target patterns) which could not be as yet systematically explained in existing models.