具有Markov切换的随机基因表达调控模型  

A Stochastic Gene Expression Regulation Model with Markov Switching

作　　者：闫博伦 唐若诗 邱志鹏[2] YAN Bolun;TANG Ruoshi;QIU Zhipeng(School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210094,China;Interdisciplinary Center for Fundamental and Frontier Sciences,Nanjing University of Science and Technology,Jiangyin 214443,China)

机构地区：[1]南京理工大学数学与统计学院,江苏南京210094 [2]南京理工大学基础前沿交叉中心,江苏江阴214443

出　　处：《山西大学学报（自然科学版）》2024年第1期122-133,共12页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(12071217)。

摘　　要：建立了一类具有白噪音和Markov切换共同驱动的基因协作表达模型。首先通过随机比较原理构建了模型的随机吸引集,结论表明环境噪音影响下系统的解最终一致有界。其后通过构造合适的Lyapunov函数证明了所研究模型拥有唯一遍历的平稳分布,且系统的解是遍历的。最后,进行了一些数值模拟来佐证所得结果,并在数值上发现所研究模型存在双稳态现象,这对细胞分化等生物学领域的研究有重要意义。Both white noise and Markov switching are introduced to study the dynamics of gene cooperative expression system.The random attraction set of the model is constructed based on the random comparison principle.The conclusion shows that the solution of the system is uniformly bounded under the influence of environmental noise.It is proved that the model has a unique ergodic stationary distribution and the solution of the system is ergodic by constructing a suitable Lyapunov function.Some numerical simulations are carried out to support the results,and the numerical results show that the bistable phenomenon exists in the model studied,which is of great significance for the research of cell differentiation and other biological fields.

关 键 词：布朗运动 保序系统 MARKOV链 随机吸引集 平稳分布 

分 类 号：O175[理学—数学] Q257[理学—基础数学]