| 基于最优控制的具时滞水体富营养化模型的稳定性与分支研究 |
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| 引用本文： | 杨纪华.基于最优控制的具时滞水体富营养化模型的稳定性与分支研究[J].贵州大学学报(自然科学版),2013(6):9-12. |
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| 作者姓名： | 杨纪华 |
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| 作者单位： | 宁夏师范学院数学与计算机科学学院,宁夏固原756000 |
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| 基金项目： | 国家自然科学基金资助项目（11031002）;宁夏自然科学基金资助项目（NZl3213）;宁夏师范学院创新团队资助项目（zy201207）;宁夏师范学院本科教学工程资助项目（JXGC2012801） |
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| 摘 要： | 研究了基于最优控制的具时滞水体富营养化系统模型。从对系统线性化方程的特征方程根的分布分析入手，讨论了系统平衡点的稳定性，确定了系统的线性稳定性区域，发现当系统中的时滞经过一系列临界值时，系统经历了Hopf分支。
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| 关 键 词： | 水体富营养化 稳定性 Hopf分支 时滞 |
Stability and Hopf Bifurcation Existence Analysis of Water Eutrophication with Time Delay Based on Optimal Control |
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| YANG Ji-hua.Stability and Hopf Bifurcation Existence Analysis of Water Eutrophication with Time Delay Based on Optimal Control[J].Journal of Guizhou University(Natural Science),2013(6):9-12. |
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| Authors: | YANG Ji-hua |
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| Institution: | YANG Ji-hua(Department of Mathematics and Computer Science, Ningxia Teachers University, Guyuan 756000, China) |
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| Abstract: | The mathematical model of water eutrophication system with time delay was studied. The stability of the equilibrium was discussed by analyzing the characteristic equation of the linearized system of original system at the equilibrium. The regions of linear stability of equilibrium were given ; it is found that Hopf bifurcation exists when the delay passes through a sequence of critical values. |
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| Keywords: | water eutrophication stability Hopf bifurcation time delay |
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