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

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 Poincaré map, we obtain some sufficient conditions of the bifurcation of periodic solutio...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2023-06, Vol.35 (2), p.1243-1271
Main Authors: Quan, Tingting, Li, Jing, Zhu, Shaotao, Sun, Min
Format: Article
Language:English
Subjects:
Applications of Mathematics
Bifurcation theory
Dynamical systems
Hamiltonian functions
Ice cover
Mathematics
Mathematics and Statistics
Nonlinear dynamics
Nonlinear systems
Orbits
Ordinary Differential Equations
Partial Differential Equations
Poincare maps
Spherical coordinates
Suspension systems
Toruses
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Summary: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 Poincaré map, we obtain some sufficient conditions of the bifurcation of periodic solutions of some 2 n -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 .
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-021-09954-8