| 具有多个参数扰动的随机恒化器模型研究 |
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| 引用本文： | 李姣,孟琳琳,原三领. 具有多个参数扰动的随机恒化器模型研究[J]. 上海理工大学学报, 2013, 35(6): 523-530 |
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| 作者姓名： | 李姣 孟琳琳 原三领 |
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| 作者单位： | 上海理工大学 理学院, 上海 200093;上海理工大学 理学院, 上海 200093;上海理工大学 理学院, 上海 200093 |
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| 基金项目： | 国家自然科学基金资助项目（11271260）；上海市重点学科建设资助项目（XTKX2012）；上海市教委科研创新重点资助项目（13ZZ116） |
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| 摘 要： | 考虑了一类营养的输入浓度和稀释率同时受到白噪声干扰的随机恒化器模型.首先证明了模型正解的全局存在唯一性；其次通过构造Lyapunov函数的方法研究了在不同条件下随机模型的解围绕其相应确定性系统的正平衡点和绝灭平衡点的振荡行为；最后通过数值仿真验证了所得结论的正确性.
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| 关 键 词： | 随机恒化器模型 布朗运动 伊藤公式 渐近行为 |
| 收稿时间： | 2012-10-04 |
Chemostat Model with Stochastic Perturbation on Multiple Parameters |
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| LI Jiao,MENG Lin-lin and YUAN San-ling. Chemostat Model with Stochastic Perturbation on Multiple Parameters[J]. Journal of University of Shanghai For Science and Technology, 2013, 35(6): 523-530 |
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| Authors: | LI Jiao MENG Lin-lin YUAN San-ling |
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| Affiliation: | College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China |
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| Abstract: | A stochastic chemostat model was considered,in which both the input concentration of nutrient and the dilution rate are simultaneously influenced by white noises,The uniqueness and global existence of the positive solution of the model were proved,and it was investigated how the solution is oscillating around the positive equilibrium and the extinction equilibrium of the corresponding deterministic model under different conditions.Numerical simulations were carried out to illustrate the conclusions. |
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| Keywords: | stochastic chemostat model Brownian motion Itô formula asymptotic behavior |
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