Stability and Limit Cycle Bifurcation for Two Kinds of Generalized Double Homoclinic Loops in Planar Piecewise Smooth Systems

被引：2
|
作者：
Liang, Feng [1 ]
Han, Maoan [2 ]
机构：
[1] Anhui Normal Univ, Inst Math, Wuhu 241000, Peoples R China
[2] Shanghai Normal Univ, Inst Math, Shanghai 200234, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2014年 / 24卷 / 12期
基金：
中国国家自然科学基金; 国家教育部博士点专项基金资助;
关键词：
Stability; bifurcation; limit cycle; piecewise smooth differential system; generalized double homoclinic loop;
D O I：
10.1142/S0218127414501533
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we present two kinds of generalized double homoclinic loops in planar piecewise smooth systems. For their stability a criterion is provided. Under nondegenerate conditions, we prove that for each case there are at most five limit cycles which can be bifurcated from the generalized double homoclinic loop. Especially, we construct two concrete systems to show that the upper bound can be achieved in both cases.
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页数：12
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