随机化学系统接近平均场模型SNIPER分岔的分析
Analysis of a stochastic chemical system close to a SNIPER bifurcation of its mean-field model
摘要：
本文提出了一个分析化学系统随机模型的框架，其中确定性平均场描述正经历一个鞍结无限周期（SNIPER）分岔。例如，在细胞周期调节的建模中出现这种分叉。结果表明，随机系统具有振荡的解决方案，即使参数值的平均场模型不振荡。这些振荡的平均周期对模型的参数（动力学速率常数）和系统的大小（存在的分子数）的依赖性进行了研究。我们的方法是基于化学Fokker-Planck方程。为了深入了解该方法的优点和缺点，首先分析了一个简单的一维化学开关，然后详细研究了化学SNIPER问题。首先，通过数值求解福克-普朗克方程得到的结果。然后渐近分析的Fokker-Planck方程是用来获得明确的公式的振荡周期作为一个函数的速率常数和作为一个函数的系统大小。
英文摘要：
A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs for example in the modelling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) is studied. Our approach is based on the chemical Fokker-Planck equation. To get some insights into advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, before the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size.
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