A Linear Estimate of the Number of Limit Cycles for A Piecewise Smooth Near-Hamiltonian System

被引：10

作者：

Chen, Xiaoyan ^{[1
,2
]}

Han, Maoan ^{[3
]}

机构：

[1] Zhejiang Normal Univ, Coll Teacher Educt, Jinhua 321004, Zhejiang, Peoples R China

[2] Cent South Univ Forestry & Technol, Coll Sci, Changsha 410004, Peoples R China

[3] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2020年 / 19卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Piecewise smooth system; Homoclinic loop; Melnikov function; Limit cycle; DISCONTINUOUS DIFFERENTIAL-SYSTEMS; ISOCHRONOUS CENTERS; BIFURCATION;

D O I：

10.1007/s12346-020-00398-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study Poincare bifurcation of limit cycles from a piecewise linear Hamiltonian system with a center at the origin and a homoclinic loop round the origin. By using the Melnikov function method, we give an estimation of the number of limit cycles which bifurcate from the period annulus between the center and the homoclinic loop under the piecewise polynomial perturbations of degree n. This result confirms a conjecture.

引用

页数：19

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