Martirosyan A, Saakian David B
Yerevan State University, Alex Manoogian 1, Yerevan 375025, Armenia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Aug;84(2 Pt 1):021122. doi: 10.1103/PhysRevE.84.021122. Epub 2011 Aug 12.
We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.
我们应用哈密顿-雅可比方程（HJE）形式主义来求解化学主方程（CME）的动力学。我们找到了（在大系统规模极限下）概率分布的精确解析表达式，包括分布方差动力学的显式表达式。我们还给出了具有时间依赖速率的模型的一些简单情况的解。我们使用一个特殊的假设从HJE方法推导出了范坎彭方法的结果。使用范坎彭方法，我们给出了一个常微分方程组（ODEs）来定义二维情况下的方差。我们对具有平稳噪声的CME进行了数值计算。我们给出了一维CME中平稳噪声情况下双稳性消失的解析判据。
