| 一类三次Kolmogorov系统的正平衡点的性态与极限环的分支实例 |
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| 引用本文： | 李星.一类三次Kolmogorov系统的正平衡点的性态与极限环的分支实例[J].邵阳学院学报(自然科学版),2010,7(4):4-8. |
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| 作者姓名： | 李星 |
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| 作者单位： | [1]广州大学数学与计算科学学院,广东广州510000 [2]广州市白云区钟落潭中学,广东广州510550 |
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| 摘 要： | 本文研究了一类三次Kolmogorov系统,对它的两个正平衡点的类型与其附近轨线的性态展开了分类研究.同时考虑了正平衡点(1,1)附近的极限环分支情况,通过作适当的变换以及运用计算机对焦点量的仔细计算,得出了该系统在小参数扰动下能够从(1,1)附近分支出3个极限环的结论.
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| 关 键 词： | 正平衡点 焦点量 Kolmogorov系统 极限环 分支 |
The Properties of the Positive Equilibrium Points of a Class of Cubic Kolmogorov System and Examples of the Bifurcation of the Limit Cycles |
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| LI Xing.The Properties of the Positive Equilibrium Points of a Class of Cubic Kolmogorov System and Examples of the Bifurcation of the Limit Cycles[J].Journal of Shaoyang University:Science and Technology,2010,7(4):4-8. |
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| Authors: | LI Xing |
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| Institution: | LI Xing ,(1.School of Mathematics and Computational Science,Guangzhou University,Guangzhou,Guangdong,510000; 2.Zhongluotan Middle School of Baiyun District,Guangzhou,Guangdong,510550) |
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| Abstract: | In this paper,a class of cubic Kolmogorov system in which two positive equilibrium points are classified is investigated.At the same time,the orbit of two equilibrium point（1,1） and（2,2） are considered.Moreover,through the appropriate transformations and the careful calculation of the focal values,the system that can occur 3 limit cycles near the positive equilibrium poin（1,1） under the small parameters disturbances is obtained. |
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| Keywords: | positive equilibrium points focal values Kolmogorov system limit cycle bifurcation |
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