Bifurcation and number of subharmonic solutions of a 4D non-autonomous slow-fast system and its application

被引：11

作者：

Li, Jing ^{[1
]}

Quan, Tingting ^{[2
]}

Zhang, Wei ^{[3
]}

机构：

[1] Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

[2] Tianjin Chengjian Univ, Sch Sci, Tianjin 300384, Peoples R China

[3] Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China

来源：

NONLINEAR DYNAMICS | 2018年 / 92卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Slow-fast system; Non-autonomous; Curvilinear coordinate; Bifurcation; Subharmonic solutions; PERIODIC-ORBITS; SINGULAR PERTURBATION; INVARIANT TORI; DIFFERENTIAL-SYSTEMS; FAST DYNAMICS; LIMIT-CYCLES; POINTS; EQUATIONS; FOLD;

D O I：

10.1007/s11071-018-4086-4

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In this paper, we study the existence and bifurcation of subharmonic solutions of a four-dimensional slow-fast system with time-dependent perturbations for the unperturbed system in two cases: one is a Hamilton system and the other has a singular periodic orbit, respectively. We perform the curvilinear coordinate transformation and construct a Poincar, map for both cases. Then some of sufficient conditions and necessary conditions of the existence and bifurcation of subharmonic solutions are obtained by analyzing the Poincar, map. We apply them to study the bifurcation of multiple subharmonic solutions of a honeycomb sandwich plate dynamics system and to discuss the number of subharmonic solutions in different bifurcation regions induced by two parameters. The maximum number of subharmonic solutions of the honeycomb sandwich plate system is 7 and the relative parameter control condition is obtained.

引用

页码：721 / 739

页数：19

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