具有一般反应函数与贴壁生长现象的随机恒化器模型的全局动力学行为

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1912-1924.

具有一般反应函数与贴壁生长现象的随机恒化器模型的全局动力学行为

刘丽雅¹(),蒋达清^1,^2,*()

¹ 中国石油大学(华东)石油工程学院非常规油气开发教育部重点实验室山东青岛 266580
² 中国石油大学(华东)理学院山东青岛 266580

收稿日期:2020-08-20 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 蒋达清 E-mail:liuliya_1993@hotmail.com;daqingjiang2010@hotmail.com
作者简介:刘丽雅, E-mail: liuliya_1993@hotmail.com
基金资助:
国家自然科学基金(11871473);中央高校基本科研业务费专项资金(15CX08011A)

Global Dynamics of a Stochastic Chemostat Model with General Response Function and Wall Growth

Liya Liu¹(),Daqing Jiang^1,^2,*()

¹ School of Petroleum Engineering, Key Laboratory of Unconventional Oil & Gas Development, China University of Petroleum (East China), Ministry of Education, Shandong Qingdao 266580
² College of Science, China University of Petroleum, Shandong Qingdao 266580

Received:2020-08-20 Online:2021-12-26 Published:2021-12-02
Contact: Daqing Jiang E-mail:liuliya_1993@hotmail.com;daqingjiang2010@hotmail.com
Supported by:
the NSFC(11871473);the Fundamental Research Funds for the Central Universities(15CX08011A)

摘要/Abstract

摘要：

该文研究了具有一般反应函数与贴壁生长现象的随机恒化器模型的全局动力学行为.一方面，得到了微生物灭绝的条件；另一方面，通过构造合适的Lyapunov函数得到了模型存在遍历的平稳分布的条件，此时微生物持久生存.最后，实例和数值模拟验证了该文的理论结果.

关键词: 恒化器, 贴壁生长, 灭绝性, 平稳分布, 一般反应函数

Abstract:

This paper deals with problems of a stochastic chemostat model with general response function and wall growth. We show the conditions for the microorganism to be extinct. On the other hand, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the model which means the microorganism can become persistent. Finally, example and numerical simulations are introduced to illustrate the analytical results.

Key words: Chemostat, Wall growth, Extinction, Stationary distribution, General response functions

中图分类号:

O211.63

刘丽雅,蒋达清. 具有一般反应函数与贴壁生长现象的随机恒化器模型的全局动力学行为[J]. 数学物理学报, 2021, 41(6): 1912-1924.

Liya Liu,Daqing Jiang. Global Dynamics of a Stochastic Chemostat Model with General Response Function and Wall Growth[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1912-1924.

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