Abstract
Abstract
In the paper we deal with a quintic Liénard system of the form
x
̇
=
y
−
(
a
1
x
+
a
2
x
3
+
a
3
x
5
)
,
y
̇
=
b
1
x
+
b
2
x
3
with a
Z
2
-symmetry, where
a
1
,
a
2
,
b
1
∈
R
and a
3
b
2 ≠ 0. A complete study of this system with b
2 > 0, called the saddle case, is finished, showing that the system exhibits at most two limit cycles, and the necessary and sufficient conditions are obtained on the existence of two limit cycles and a two-saddle heteroclinic loop. We also present a global bifurcation diagram and the corresponding phase portraits of this system, including Hopf bifurcation, Bautin bifurcation, two-saddle heteroclinic loop bifurcation and double limit cycle bifurcation.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Shanghai
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
10 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献