Stochastic simulation of chemical chaos

Abstract

Our stochastic simulations of Willamowski-Rossler indicated that the macroscopic rate equations of chemical kinetics can satisfactorily describe the microscopic reaction processes in the vicinity of nonequilibrium stable steady states and limit cycles. However, in the presence of chaos, the chemical kinetic rate equations cease to be useful even though they still serve to tell when they become invalid. From the viewpoint of stochastic theory, a chemical reaction process can be well described by the Master equation, and the usual macroscopic rate equation is only its first-order approximation when the system is enlarged to infinite[5]. When the system approaches one of its bifurcation points, the formerly trivial fluctuations can now grow to macroscopic size and make the macroscopic variables lose their meanings. The simulation of a chemical chaos of this report has shown that the time evolution of averaged molecular numbers of direct simulation has nothing in common with trajectories predicted by rate equations. Therefore the first-order approximation of the Master equation is no longer sufficient to describe the true reaction processes when the rate equations display chaotic dynamics: These suggest that a microscopic or mesoscopic approach is necessary at this point. Further investigation toward the microscopic aspect of a reaction when its chemical rate law predicts chaos is always desired.