Cubic Liénard equations with quadratic damping having two antisaddles

被引：0
|
作者：
Dumortier F. [1 ]
Kooij R.E. [2 ]
Li C. [3 ]
机构：
[1] Limburgs Universitair Centrum, B-3590 Diepenbeek, Universitaire Campus
[2] KPN Research, 2260 AK Leidschendam
[3] Department of Mathematics and Institute of Mathematics, Peking University
来源：
Qualitative Theory of Dynamical Systems | 2000年 / 1卷 / 2期
关键词：
Quadratic System; Weak Singularity; Weak Focus; Unique Singularity; Dulac Function;
D O I：
10.1007/BF02969477
中图分类号：
学科分类号：
摘要：
The paper deals with differential equations of the form ẋ =y, ẏ= -g(x)-f(x)y, with f and g polynomials of degree respectively two and three. They are called cubic Liénard equations with quadratic damping. Attention goes to the case in which the equations have three singular points of which one is a saddle and two are antisaddles. A lot of results are given on the upper-bound for the number of limit cycles, depending on the relative position of the zeros off andg on the x-axis. © 2000 Birkhäuser-Verlag.
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页码：163 / 209
页数：46
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