Limit Cycles Near a Piecewise Smooth Generalized Homoclinic Loop with a Nonelementary Singular Point

被引:2
作者
Liang, Feng [1 ]
Yang, Junmin [2 ]
机构
[1] Anhui Normal Univ, Inst Math, Wuhu 241000, Peoples R China
[2] Hebei Normal Univ, Inst Math, Shijiazhuang 050024, Peoples R China
来源
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2015年 / 25卷 / 13期
基金
中国国家自然科学基金;
关键词
Limit cycle; piecewise Hamiltonian system; generalized homoclinic loop; Melnikov method; BIFURCATIONS;
D O I
10.1142/S021812741550176X
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we deal with limit cycle bifurcations by perturbing a piecewise smooth Hamiltonian system with a generalized homoclinic loop passing through a nonelementary singular point. We first give an expansion of the first Melnikov function corresponding to a period annulus near the generalized homoclinic loop. Then, based on the first coefficients in the expansion we obtain a lower bound for the maximal number of limit cycles bifurcated from the period annulus. As applications, two concrete systems are considered.
引用
收藏
页数:22
相关论文
共 25 条
[11]   Melnikov method for homoclinic bifurcation in nonlinear impact oscillators [J].
Du, ZD ;
Zhang, WN .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 50 (3-4) :445-458
[12]   Center-focus problem for discontinuous planar differential equations [J].
Gasull, A ;
Torregrosa, J .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (07) :1755-1765
[13]  
Han M., 2013, Bifurcation Theory of Limit Cycles
[14]  
Han M. A., 2012, INT J BIFURCAT CHAOS, V22
[15]   On the number of limit cycles in near-hamiltonian polynomial systems [J].
Han, Maoan ;
Chen, Guanrong ;
Sun, Chengjun .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2007, 17 (06) :2033-2047
[16]  
Han MA, 2015, J APPL ANAL COMPUT, V5, P809
[17]   On Hopf bifurcation in non-smooth planar systems [J].
Han, Maoan ;
Zhang, Weinian .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (09) :2399-2416
[18]  
Kunze M., 2000, Non-smooth Dynamical Systems
[19]   Bifurcation of limit cycles from generalized homoclinic loops in planar piecewise smooth systems [J].
Liang, Feng ;
Han, Maoan ;
Zhang, Xiang .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (12) :4403-4436
[20]   THE STABILITY OF SOME KINDS OF GENERALIZED HOMOCLINIC LOOPS IN PLANAR PIECEWISE SMOOTH SYSTEMS [J].
Liang, Feng ;
Han, Maoan .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2013, 23 (02)