The characteristics of Langevin equations for the intrinsic fluctuations of chemical reactions are investigated via the analyses on the Brusselator model in the parameter domain of spirally stable focus. Two forms of Langevin equations are shown to be equivalent for the results of two statistical measures. The comparisons in the results of two measures between Langevin equations and chemical master equation are given: The difference in stationary probability densities is significant for systems close to the bifurcation point, even the system size is large; the power spectra of Langevin equations with white noise are qualitatively the same as that of chemical master equation, but the discrepancy is found between Langevin equations with colored noises and chemical master equation, if the length of correlation-time is comparable with the correlation-time of a system. As the linearized Langevin equations possess singularity at the supercritical Hopf bifurcation point for the statistical measures, the Langevin equations displace the bifurcation points, and the amount of displacement is a decreasing function of the system size and the length of correlation-time of noises.

通过对螺旋稳定焦点参数域中的Brusselator模型的分析，研究了化学反应固有波动的Langevin方程的特征。对于两种统计量度的结果，两种形式的Langevin方程等效。给出了Langevin方程和化学主方程之间的两种测量结果的比较：对于接近分叉点的系统，即使系统规模很大，固定概率密度的差异也很明显；从本质上讲，具有白噪声的Langevin方程的功率谱与化学主方程的功率谱相同，但在有色噪声的Langevin方程与化学主方程之间存在差异，如果相关时间的长度与系统的相关时间相当。由于线性化的Langevin方程在统计测量的超临界Hopf分支点处具有奇异性，因此Langevin方程会置换分支点，并且位移量是系统大小和噪声相关时间长度的递减函数。