| 一类平面E_3系统的全局结构 |
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| 引用本文： | 殷先军. 一类平面E_3系统的全局结构[J]. 北京理工大学学报, 1988, 0(3) |
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| 作者姓名： | 殷先军 |
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| 作者单位： | 北京工业学院应用数学系 |
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| 摘 要： | 本文研究平面三次系统 (dx)/(dt)=sum from 1≤i+j≤3 a_(i j)X~iy~j (dy)/(dt)=sum from 1≤i+j≤3 b_(i j)X~iy~j [E_3] 在x~2+y~2=1,y=K_1,y=K_2为(E_3)的代数轨线(可以相交)的假定下,研究了(E_3)全局结构,得出了极限环的存在唯一性及分界线环的存在性,给出了此类系统高阶奇点类型的一种简捷的判别法。
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| 关 键 词： | 代数轨线 全局结构 极限环 奇点 旋转向量场 |
GLOBAL STRUCTURE OF A CLASS OF PLANAR CUBIC SYSTEM(E3) |
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| Yin Xianjun. GLOBAL STRUCTURE OF A CLASS OF PLANAR CUBIC SYSTEM(E3)[J]. Journal of Beijing Institute of Technology(Natural Science Edition), 1988, 0(3) |
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| Authors: | Yin Xianjun |
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| Affiliation: | Department of Applied Mathematics |
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| Abstract: | A class of planar cubic (E3)with three algebraic orbits x2 + y2 = 1,y = k1, y = k2 is studied. The global structure of (E3) is discussed, the existence and uniqueness of limit cycle and the existence of singular closed orbits are obtained. A easy criteria for determining the type of sigular point of high order is given. |
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| Keywords: | algebraic orbit global structure limit cycle sigular point rotated vector field. |
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