On the nonexistence, existence and uniqueness of limit cycles

被引：139

作者：

Giacomini, H ^{[1
]}

Llibre, J ^{[1
]}

Viano, M ^{[1
]}

机构：

[1] UNIV AUTONOMA BARCELONA,DEPT MATEMAT,E-08193 BARCELONA,SPAIN

来源：

NONLINEARITY | 1996年 / 9卷 / 02期

关键词：

D O I：

10.1088/0951-7715/9/2/013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present two new criteria for studying the nonexistence, existence and uniqueness of limit cycles of planar vector fields. We apply these criteria to some families of quadratic and cubic polynomial vector fields, and to compute an explicit formula for the number of limit cycles which bifurcate out of the linear centre x = -y, y, = x, when we deal with the system x = -y + epsilon Sigma(i+j=1)(n) a(ij)x(i)y(j), y = x + epsilon Sigma(i+j=1)(n) b(ij)x(i)y(j). Moreover, by using the second criterion we present a method to derive the shape of the bifurcated limit cycles from a centre.

引用

页码：501 / 516

页数：16