Bifurcation and Number of Periodic Solutions of Some 2n-Dimensional Systems and Its Application

Autor:	Shaotao Zhu, Tingting Quan, Min Sun, Jing Li
Rok vydání:	2021
Předmět:	Curvilinear coordinates 010102 general mathematics Mathematical analysis 01 natural sciences Hamiltonian system 010101 applied mathematics Nonlinear system Bifurcation theory Ordinary differential equation 0101 mathematics Invariant (mathematics) Analysis Bifurcation Mathematics Poincaré map
Zdroj:	Journal of Dynamics and Differential Equations. 35:1243-1271
ISSN:	1572-9222 1040-7294
DOI:	10.1007/s10884-021-09954-8
Popis:	In high dimension, the bifurcation theory of periodic orbits of nonlinear dynamics systems are difficult to establish in general. In this paper, by performing the curvilinear coordinate frame and constructing a Poincare map, we obtain some sufficient conditions of the bifurcation of periodic solutions of some 2n-dimensional systems for the unperturbed system in two cases: one is a decoupled n-degree-of-freedom nonlinear Hamiltonian system and the other has an isolated invariant torus. We use a new method and study new types of systems compared with the existing results. As an application we study the bifurcation and number of periodic solutions of an ice covered suspension system. Under a certain parametrical condition, the number of periodic solutions of this system can be 2 or 1 with the variation of parameter $$p_{2}$$ .
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a7c5262d0edeb515fc9ea106dd82c4e9 https://doi.org/10.1007/s10884-021-09954-8 Zobrazit plný text záznamu Full text from SpringerLink