Internal fluctuations, period doubling, and chemical chaos

The effects of internal molecular fluctuations on period-doubling bifurcations and chaotic band merging are studied in a well-stirred reactive chemical system where spatial degrees of freedom play no role. The calculations are carried out using a stochastic model based on reactive lattice-gas cellular automata. Molecular fluctuations arising from reactive collisions are incorporated in the model and the mass-action rate equations are recovered in the mean field limit. Large system sizes can be studied and permit the investigation of the internal noise scaling structure in the periodic and chaotic regimes. For the Willamowski-R\"ossler system the noise scaling exponent is consistent with that found for one-dimensional quadratic maps subject to external noise. The model provides a means to study small, non- equilibrium, reacting systems where fluctuations may not be neglected.