Dynamical behaviors of a stochastic multi-molecule biochemical reaction model with Ornstein-Uhlenbeck process

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-08-06 DOI:10.1007/s10910-024-01653-1

Ying Yang, Jing Guo

引用次数: 0

Abstract

In this paper, we develop a stochastic multi-molecule chemical reaction model with reaction rate perturbed by log-normal \(Ornstein-Uhlenbeck\) process in order to consider the effects of random factors on chemical reaction dynamics. Firstly, we prove the existence and uniqueness of the global positive solution for the stochastic model. In addition, we obtain the conditions under which the corresponding stochastic system exist a stationary distribution. Then, we derive a sufficient condition to end the reaction. Furthermore, the stochastic system has been transformed into a linearized system, by solving \(Fokker-Planck\) equation, we obtain the exact expression of the density function around the quasi-equilibrium of this system. Finally, we draw a conclusion that the dynamical behaviors of the stochastic system will be affected by random factor, \(Ornstein-Uhlenbeck\) process respectively

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具有 Ornstein-Uhlenbeck 过程的随机多分子生化反应模型的动力学行为

本文建立了一个反应速率受对数正态（Ornstein-Uhlenbeck）过程扰动的随机多分子化学反应模型，以考虑随机因素对化学反应动力学的影响。首先，我们证明了随机模型全局正解的存在性和唯一性。此外，我们还得到了相应随机系统存在静态分布的条件。然后，我们推导出反应结束的充分条件。此外，将随机系统转化为线性化系统，通过求解（Fokker-Planck）方程，我们得到了该系统准平衡点附近密度函数的精确表达式。最后，我们得出结论：随机系统的动力学行为将分别受到随机因素、（Ornstein-Uhlenbeck）过程的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.