| 污染环境中Smith模型的稳定性 |
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| 引用本文： | 李冬梅,尹晓,邵琛. 污染环境中Smith模型的稳定性[J]. 哈尔滨理工大学学报, 2011, 16(3): 98-103 |
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| 作者姓名： | 李冬梅 尹晓 邵琛 |
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| 作者单位： | 哈尔滨理工大学应用科学学院,黑龙江哈尔滨,150080 |
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| 基金项目： | 黑龙江省自然科学基金(A200502)；黑龙江省教育厅计划项目 |
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| 摘 要： | 针对小容量污染环境中的种群生存问题,考虑了环境毒素浓度和体内毒素浓度受死亡种群的影响,研究了一类外界毒素输入率是常数的污染环境中单种群Smith模型.给出了平衡点存在条件,利用Ruth-Hurwitz准则和复合矩阵理论的分析方法,讨论了平衡点的局部稳定性及全局稳定性.
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| 关 键 词： | Smith模型 污染环境 平衡点 局部稳定 全局稳定 |
The Stability of Smith's Model in a Polluted Environment |
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| LI Dong-mei,YIN Xiao,SHAO Chen. The Stability of Smith's Model in a Polluted Environment[J]. Journal of Harbin University of Science and Technology, 2011, 16(3): 98-103 |
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| Authors: | LI Dong-mei YIN Xiao SHAO Chen |
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| Affiliation: | (School of Applied Science,Harbin University of Science and Technology,Harbin 150080,China) |
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| Abstract: | In view of the species survival problem in polluted environment of small capacity, considering the effect of the variance of the dead population on the internal and environmental toxicant density, the Smith＇ s model with constant input rate of toxin in polluted environment is studied. The existence conditions of the positive equilib- rium is identified, by using Ruth-Hurwitz criterion and the analysis method of complex matrix theory, the local sta- bility and the global stability of equilibriums are discussed. |
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| Keywords: | Smith＇ s model polluted environment equilibrium local stability global stability |
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