Stochastic simulation of chemical chaos |
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Authors: | Hongli Wang Houwen Xin |
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Institution: | (1) Department of Chemical Physics, University of Science and Technology of China, 230026 Hefei, China |
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Abstract: | Conclusion 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 infinite5]. 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. |
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Keywords: | chaos stochastic simulation nonequilibrium |
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