Bifurcation of periodic orbits by perturbing high-dimensional piecewise smooth integrable systems

被引：77

作者：

Tian, Huanhuan ^{[1
]}

Han, Maoan ^{[1
,2
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 11期

基金：

中国国家自然科学基金;

关键词：

High-dimensional system; Melnikov function; Periodic orbit; Bifurcation; LIMIT-CYCLE BIFURCATIONS; HAMILTONIAN-SYSTEMS;

D O I：

10.1016/j.jde.2017.08.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with the problem of periodic orbit bifurcations for high-dimensional piecewise smooth systems. Under the assumption that the unperturbed system has a family of periodic orbits which are transversal to the switch plane, a formula for the first order Melnikov vector function is developed which can be used to study the number of periodic orbits bifurcated from the periodic orbits. We especially can use the function to study the number of periodic orbits both in degenerate Hopf bifurcations and in degenerate homoclinic bifurcations. Finally, we present two examples to illustrate an application of the theoretical results. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：7448 / 7474

页数：27

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