Unstable periodic orbits analysis in the Qi system

doi:10.1088/1674-1056/aca9c3

中国物理B ›› 2023, Vol. 32 ›› Issue (4): 40502-040502.doi: 10.1088/1674-1056/aca9c3

Unstable periodic orbits analysis in the Qi system

Lian Jia(贾莲), Chengwei Dong(董成伟)^†, Hantao Li(李瀚涛)^‡, and Xiaohong Sui(眭晓红)

Department of Physics, North University of China, Taiyuan 030051, China

收稿日期:2022-09-26 修回日期:2022-11-15 接受日期:2022-12-08 出版日期:2023-03-10 发布日期:2023-03-30
通讯作者: Chengwei Dong, Hantao Li E-mail:dongchengwei@tsinghua.org.cn;lihantao@nuc.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12205257, 11647085, and 11647086), the Shanxi Province Science Foundation for Youths (Grant No. 201901D211252), Fundamental Research Program of Shanxi Province (Grant No. 202203021221095), and the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi of China (Grant Nos. 2019L0505, 2019L0554, and 2019L0572).

Unstable periodic orbits analysis in the Qi system

Lian Jia(贾莲), Chengwei Dong(董成伟)^†, Hantao Li(李瀚涛)^‡, and Xiaohong Sui(眭晓红)

Department of Physics, North University of China, Taiyuan 030051, China

Received:2022-09-26 Revised:2022-11-15 Accepted:2022-12-08 Online:2023-03-10 Published:2023-03-30
Contact: Chengwei Dong, Hantao Li E-mail:dongchengwei@tsinghua.org.cn;lihantao@nuc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12205257, 11647085, and 11647086), the Shanxi Province Science Foundation for Youths (Grant No. 201901D211252), Fundamental Research Program of Shanxi Province (Grant No. 202203021221095), and the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi of China (Grant Nos. 2019L0505, 2019L0554, and 2019L0572).

摘要/Abstract

摘要： We use the variational method to extract the short periodic orbits of the Qi system within a certain topological length. The chaotic dynamical behaviors of the Qi system with five equilibria are analyzed by the means of phase portraits, Lyapunov exponents, and Poincaré maps. Based on several periodic orbits with different sizes and shapes, they are encoded systematically with two letters or four letters for two different sets of parameters. The periodic orbits outside the attractor with complex topology are discovered by accident. In addition, the bifurcations of cycles and the bifurcations of equilibria in the Qi system are explored by different methods respectively. In this process, the rule of orbital period changing with parameters is also investigated. The calculation and classification method of periodic orbits in this study can be widely used in other similar low-dimensional dissipative systems.

关键词: chaos, periodic orbits, bifurcation, Qi system

Abstract: We use the variational method to extract the short periodic orbits of the Qi system within a certain topological length. The chaotic dynamical behaviors of the Qi system with five equilibria are analyzed by the means of phase portraits, Lyapunov exponents, and Poincaré maps. Based on several periodic orbits with different sizes and shapes, they are encoded systematically with two letters or four letters for two different sets of parameters. The periodic orbits outside the attractor with complex topology are discovered by accident. In addition, the bifurcations of cycles and the bifurcations of equilibria in the Qi system are explored by different methods respectively. In this process, the rule of orbital period changing with parameters is also investigated. The calculation and classification method of periodic orbits in this study can be widely used in other similar low-dimensional dissipative systems.

Key words: chaos, periodic orbits, bifurcation, Qi system

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Ac (Low-dimensional chaos) 02.60.Cb (Numerical simulation; solution of equations)

Lian Jia(贾莲), Chengwei Dong(董成伟), Hantao Li(李瀚涛), and Xiaohong Sui(眭晓红). Unstable periodic orbits analysis in the Qi system[J]. 中国物理B, 2023, 32(4): 40502-040502.

Lian Jia(贾莲), Chengwei Dong(董成伟), Hantao Li(李瀚涛), and Xiaohong Sui(眭晓红). Unstable periodic orbits analysis in the Qi system[J]. Chin. Phys. B, 2023, 32(4): 40502-040502.

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Unstable periodic orbits analysis in the Qi system

Unstable periodic orbits analysis in the Qi system

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