Master equation analysis of deterministic chemical chaos

摘要

The underlying microscopic dynamics of deterministic chemical chaos was investigated in this paper. We analyzed the master equation for the Williamowski-Rossler model by direct stochastic simulation as well as in the generating function representation. Simulation within an ensemble revealed that in the chaotic regime the deterministic mass action kinetics is related neither to the ensemble mean nor to the most probable value within the ensemble. Cumulant expansion analysis of the master equation also showed that the molecular fluctuations do not admit bounded values but increase linearly in time infinitely, indicating the meaninglessness of the chaotic trajectories predicted by the phenomenological equations. These results proposed that the macroscopic description is no longer useful in the chaotic regime and a more microscopic description is necessary in this circumstance. (C) 1998 American Institute of Physics. [References: 17]