Bifurcations of invariant torus and knotted periodic orbits for the generalized Hopf-Langford system

被引：2
|
作者：
Fu, Yanggeng [1 ]
Li, Jibin [1 ,2 ]
机构：
[1] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Fujian, Peoples R China
[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
来源：
NONLINEAR DYNAMICS | 2021年 / 106卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Bifurcation; Exact solution; Knotted periodic orbit; Invariant tours; Generalized Hopf-Langford system; CHAOTIC BEHAVIOR;
D O I：
10.1007/s11071-021-06839-9
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 bifurcations of invariant torus and knotted periodic orbits for the generalized Hopf-Langford system. By using bifurcation theory of dynamical systems, we obtain the exact explicit form of the heteroclinic orbits and knot periodic orbits. Moreover, under small perturbation, we prove that the perturbed planar system has two symmetric stable limit cycles created by Poincare bifurcations. Therefore, the corresponding three-dimensional perturbed system has an attractive invariant rotation torus.
引用
收藏
页码：2097 / 2105
页数：9
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