| 污染环境中时滞种群模型的Hopf分支分析 |
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| 引用本文： | 高丽娟,廖茂新,王珠峰.污染环境中时滞种群模型的Hopf分支分析[J].南华大学学报(自然科学版),2019,33(1):29-34. |
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| 作者姓名： | 高丽娟 廖茂新 王珠峰 |
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| 作者单位： | 南华大学 数理学院,中国 衡阳 421001,南华大学 数理学院,中国 衡阳 421001,南华大学 数理学院,中国 衡阳 421001 |
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| 基金项目： | 湖南省自然科学基金项目(13JJ3075)；湖南省教育厅重点项目(17A181)；南华大学研究生科学基金项目(2018KYY093) |
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| 摘 要： | 考虑种群对毒物反应及毒物侵入人体的两个时滞,提出了一个描述污染环境中时滞种群的适当模型,运用泛函微分方程稳定性理论和分支理论,分析了正平衡点的局部稳定性及出现Hopf分支的条件。运用Matlab进行数值模拟,验证理论分析的结果。
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| 关 键 词： | 污染环境 种群模型 时滞 稳定性 Hopf分支 |
| 收稿时间： | 2018/8/26 0:00:00 |
Hopf Bifurcation Analysis of a Delay Population Model in a Polluted Environment |
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| GAO Lijuan,LIAO Maoxin and WANG Zhufeng.Hopf Bifurcation Analysis of a Delay Population Model in a Polluted Environment[J].Journal of Nanhua University:Science and Technology,2019,33(1):29-34. |
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| Authors: | GAO Lijuan LIAO Maoxin and WANG Zhufeng |
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| Institution: | School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China,School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China and School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China |
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| Abstract: | Considering the two delays of population reaction to poison and poison invasion into human body,a suitable model for describing the population with delays in polluted environment is proposed.By using the stability theory of functional differential equations and bifurcation theory,the local stability of positive equilibrium and the conditions for Hopf bifurcation are analyzed.Matlab is used to carry out numerical simulation to verify the theoretical analysis results. |
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| Keywords: | environmental pollution population model delay stability Hopf bifurcation |
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