Limit Cycles from Perturbing a Piecewise Smooth System with a Center and a Homoclinic Loop

被引：0
|
作者：
Ke, Ai [1 ]
Han, Maoan [2 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2021年 / 31卷 / 10期
关键词：
Limit cycle; bifurcation; isochronous center; Melnikov function; PERIODIC-SOLUTIONS; BIFURCATIONS; NUMBER; HOPF;
D O I：
10.1142/S0218127421501595
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study bifurcations of limit cycles arising after perturbations of a special piecewise smooth system, which has a center and a homoclinic loop. By using the Picard-Fuchs equation, we give an upper bound of the maximum number of limit cycles bifurcated from the period annulus between the center and the homoclinic loop. Furthermore, by applying the method of first-order Melnikov function we obtain a lower bound of the maximum number of limit cycles bifurcated from the center.
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页数：15
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