[1]孙明娟,董庆来.一类随机恒化器系统的动力学行为[J].深圳大学学报理工版,2016,33(4):425-431.[doi:10.3724/SP.J.1249.2016.04425]
 Sun Mingjuan and Dong Qinglai.Dynamical behavior of a stochastic ratio-dependent Chemostat model[J].Journal of Shenzhen University Science and Engineering,2016,33(4):425-431.[doi:10.3724/SP.J.1249.2016.04425]
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一类随机恒化器系统的动力学行为()
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《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第33卷
期数:
2016年第4期
页码:
425-431
栏目:
数学与应用数学
出版日期:
2016-07-12

文章信息/Info

Title:
Dynamical behavior of a stochastic ratio-dependent Chemostat model
文章编号:
201604012
作者:
孙明娟董庆来
延安大学数学与计算机科学学院, 陕西延安 716000
Author(s):
Sun Mingjuan and Dong Qinglai
School of Mathematics and Computer Science, Yan’an University, Yan’an 716000, Shaanxi Province, P.R.China
关键词:
随机微分方程 比率型功能反应函数 随机恒化器系统 随机渐近稳定 It公式 动力学行为
Keywords:
stochastic differential equation ratio-dependent functional response stochastic Chemostat stochastically asymptotic stable It formula dynamical behavior
分类号:
O 175
DOI:
10.3724/SP.J.1249.2016.04425
文献标志码:
A
摘要:
研究随机噪声对微生物连续培养的影响,引入白噪声描述营养消耗率受随机噪声的干扰,建立一类具有比率型功能反应函数的随机恒化器模型. 通过构造Lyapunov函数,利用It公式证明系统正解的全局存在唯一性,并论证了系统的绝灭平衡点是全局随机渐近稳定的;探讨了噪声强度大小对随机模型的解围绕相应确定性模型的平衡点振荡行为的影响.通过数值模拟验证所得理论结果的正确性.
Abstract:
To explore the influence of random noise on microbial continuous culture, we establish a stochastic Chemostat model with ratio-dependent functional response in which white noise is introduced to describe nutrition conversion rate influenced by random noise. By constructing stochastic Lyapunov function and using the It formula, we prove that there is a unique positive solution in the system with positive initial value, and the washout equilibrium is stochastically asymptotic stable. Furthermore, we investigate the impact of white noise on the behavior of the solution spirals around the positive equilibrium of deterministic system. The numerical simulations support the proposed theoretical results.

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备注/Memo

备注/Memo:
Received:2015-12-02;Accepted:2016-04-29
Foundation:National Natural Science Foundation of China (11471007); Natural Science Foundation of Yan’an University (YDKY201314)
Corresponding author:Associate professor Dong Qinglai.E-mail: qinglaidong@163.com
Citation:Sun Mingjuan, Dong Qinglai.Dynamical behavior of a stochastic ratio-dependent Chemostat model[J]. Journal of Shenzhen University Science and Engineering, 2016, 33(4): 425-431.(in Chinese)
基金项目:国家自然科学基金资助项目(11471007); 延安大学自然科学基金资助项目(YDKY201314)
作者简介:孙明娟(1981—),女,延安大学讲师.研究方向:应用概率统计. E-mail:sunmingjuan0535@163.com
引文:孙明娟,董庆来.一类随机恒化器系统的动力学行为[J]. 深圳大学学报理工版,2016,33(4):425-431.
更新日期/Last Update: 2016-06-23