Bifurcation of Multiple Periodic Solutions for a Class of Nonlinear Dynamical Systems in (m+4)-Dimension

被引：0

作者：

Quan, Tingting ^{[1
]}

Li, Jing ^{[2
]}

Sun, Min ^{[1
]}

Chen, Yongqiang ^{[1
]}

机构：

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

[2] Beijing Univ Technol, Interdisciplinary Res Inst, Fac Sci, Beijing 100124, Peoples R China

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2024年 / 31卷 / 01期

基金：

中国国家自然科学基金;

关键词：

( m+4 ) -dimension; Bifurcation; Curvilinear coordinate; Extended Melnikov function; Periodic solutions; SLOW-FAST SYSTEM; LIMIT-CYCLES; SUBHARMONIC SOLUTIONS; DIFFERENTIAL-SYSTEMS; 4-DIMENSIONAL CENTER; HAMILTONIAN-SYSTEMS; INVARIANT TORI; ORBITS; NUMBER;

D O I：

10.1007/s44198-024-00181-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a curvilinear coordinate transformation to study the bifurcation of periodic solutions from a 2-degree-of-freedom Hamiltonian system, when it is perturbed in Rm+4 , where m represents any positive integer. The extended Melnikov function is obtained by constructing a Poincar & eacute; map on the curvilinear coordinate frame of the trajectory of the unperturbed system. Then the criteria for bifurcation of periodic solutions of these Hamiltonian systems under isochronous and non-isochronous conditions are obtained. As for its application, we study the number of periodic solutions of a composite piezoelectric cantilever rectangular plate system whose averaged equation can be transformed into a (2+4)-dimensional dynamical system. Furthermore, under the two resonance conditions of 1:1 and 1:2, we obtain the periodic solution numbers of this system with the variation of para-metric excitation coefficient p(1).

引用

页数：24

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