The Stability of Smith’s Model in a Polluted Environment

LI Dong-mei; YIN Xiao; SHAO Chen

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The Stability of Smith’s Model in a Polluted Environment

更新时间：2026-07-10

- The Stability of Smith’s Model in a Polluted Environment
- Vol. 16, Issue 3, Pages: 98-103(2011)
- 作者机构：
  
  哈尔滨理工大学应用科学学院
- 作者简介：
- 基金信息：
- DOI：
  CLC： O175.13
- Published：2011
- 稿件说明：
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LI Dong-mei, YIN Xiao, SHAO Chen. The Stability of Smith’s Model in a Polluted Environment[J]. 2011, 16(3): 98-103.
DOI：

LI Dong-mei, YIN Xiao, SHAO Chen. The Stability of Smith’s Model in a Polluted Environment[J]. 2011, 16(3): 98-103. DOI：

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.

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 equilibrium is identified

by using Ruth-Hurwitz criterion and the analysis method of complex matrix theory

the local stability and the global stability of equilibriums are discussed.

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School of Aoolicd Sciences , Harbin Univcrsit}’ of Science and ’Ccchnoloa}’

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