| 一类微分方程系统正平衡解的存在性与全局稳定性 |
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| 引用本文： | 刘婧,马雁.一类微分方程系统正平衡解的存在性与全局稳定性[J].数学研究及应用,2007,27(4):819-825. |
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| 作者姓名： | 刘婧 马雁 |
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| 作者单位： | 大连海事大学数学系,辽宁,大连,116026 |
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| 摘 要： | 本文研究了一个自治的非线性微分方程系统,得到了系统正平衡点存在唯一的充分条件,通过伸缩变换法讨论了正平衡点局部稳定性,并运用构造Liapunov函数方法得到了它的全局渐近稳定性.
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| 关 键 词： | 食物链模型 正平衡点 伸缩变换 Liapunov函数 全局渐近稳定. |
| 文章编号： | 1000-341X（2007）04-0819-07 |
| 收稿时间： | 2006/11/7 0:00:00 |
| 修稿时间： | 2006-11-07 |
Existence and Global Stability of Positive Equilibrium Point to a System of Differential Equations |
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| LIU Jing and MA Yan.Existence and Global Stability of Positive Equilibrium Point to a System of Differential Equations[J].Journal of Mathematical Research with Applications,2007,27(4):819-825. |
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| Authors: | LIU Jing and MA Yan |
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| Institution: | Department of Mathematics, Dalian Maritime University, Liaoning 116026, China;Department of Mathematics, Dalian Maritime University, Liaoning 116026, China |
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| Abstract: | This paper deals with an autonomous nonlinear system of differential equations.We obtain the existence-uniqueness of positive equilibrium point to the problem,and then establish the local sta- bility and the global asymptotic stability of the positive equilibrium point by means of the stretching method and the Liapunove function method,respectively. |
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| Keywords: | food chain model positive steady-state stretching Liapunov function global asymptotical stability |
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