LIMIT-CYCLES OF GENERALIZED LIENARD EQUATIONS

被引:23
作者
LYNCH, S
机构
[1] Department of Mathematics and Physics, Manchester Metropolitan University Manchester
关键词
LIENARD EQUATION; LIMIT CYCLES; BIFURCATIONS;
D O I
10.1016/0893-9659(95)00078-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The generalized Lienard equations of the form: x = h(y) = F(x), y = -g(x), where F, g, and h are polynomials, are examined. It has been found that the results given by Blows, Lloyd and Lynch [1-5] for Lienard equations hold also for the generalized systems. A new result is also presented within this article.
引用
收藏
页码:15 / 17
页数:3
相关论文
共 14 条
[1]   BIFURCATION OF LIMIT-CYCLES FROM CENTERS AND SEPARATRIX CYCLES OF PLANAR ANALYTIC SYSTEMS [J].
BLOWS, TR ;
PERKO, LM .
SIAM REVIEW, 1994, 36 (03) :341-376
[2]   BIFURCATION AT INFINITY IN POLYNOMIAL VECTOR-FIELDS [J].
BLOWS, TR ;
ROUSSEAU, C .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 104 (02) :215-242
[3]   CUBIC LIENARD EQUATIONS WITH LINEAR DAMPING [J].
DUMORTIER, F ;
ROUSSEAU, C .
NONLINEARITY, 1990, 3 (04) :1015-1039
[4]  
Lins A., 1977, LECT NOTES MATH, P335
[5]   SMALL-AMPLITUDE LIMIT-CYCLES OF CERTAIN LIENARD SYSTEMS [J].
LLOYD, NG ;
LYNCH, S .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1988, 418 (1854) :199-208
[6]  
LLOYD NG, 1984, MATH P CAMB PHILOS S, V95, P359
[7]   SMALL AMPLITUDE LIMIT-CYCLES OF THE GENERALIZED MIXED RAYLEIGH-LIENARD OSCILLATOR [J].
LYNCH, S .
JOURNAL OF SOUND AND VIBRATION, 1994, 178 (05) :615-620
[8]  
LYNCH S, 1990, CALCOLO, V127
[9]  
LYNCH S, 1994, J EGYPT MATH SOC, V2, P75
[10]   THE LIMIT-CYCLE OF THE VAN DER POL EQUATION IS NOT ALGEBRAIC [J].
ODANI, K .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 115 (01) :146-152