中国物理B ›› 2022, Vol. 31 ›› Issue (1): 10501-010501.doi: 10.1088/1674-1056/ac0a61

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Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system

Yue Li(李月)1, Zengqiang Chen(陈增强)1, Zenghui Wang(王增会)2, and Shijian Cang(仓诗建)3,†   

  1. 1 College of Artificial Intelligence, Nankai University, Tianjin 300350, China;
    2 Department of Electrical and Mining Engineering, University of South Africa, Florida 1710, South Africa;
    3 Department of Product Design, Tianjin University of Science and Technology, Tianjin 300222, China
  • 收稿日期:2021-04-13 修回日期:2021-05-18 接受日期:2021-06-11 出版日期:2021-12-03 发布日期:2021-12-14
  • 通讯作者: Shijian Cang E-mail:sj.cang@gmail.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61973175 and 61873186), the South African National Research Foundation (Grant No. 132797), the South African National Research Foundation Incentive (Grant No. 114911), and the South African Eskom Tertiary Education Support Programme.

Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system

Yue Li(李月)1, Zengqiang Chen(陈增强)1, Zenghui Wang(王增会)2, and Shijian Cang(仓诗建)3,†   

  1. 1 College of Artificial Intelligence, Nankai University, Tianjin 300350, China;
    2 Department of Electrical and Mining Engineering, University of South Africa, Florida 1710, South Africa;
    3 Department of Product Design, Tianjin University of Science and Technology, Tianjin 300222, China
  • Received:2021-04-13 Revised:2021-05-18 Accepted:2021-06-11 Online:2021-12-03 Published:2021-12-14
  • Contact: Shijian Cang E-mail:sj.cang@gmail.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61973175 and 61873186), the South African National Research Foundation (Grant No. 132797), the South African National Research Foundation Incentive (Grant No. 114911), and the South African Eskom Tertiary Education Support Programme.

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摘要： The thermostatted system is a conservative system different from Hamiltonian systems, and has attracted much attention because of its rich and different nonlinear dynamics. We report and analyze the multiple equilibria and curve axes of the cluster-shaped conservative flows generated from a generalized thermostatted system. It is found that the cluster-shaped structure is reflected in the geometry of the Hamiltonian, such as isosurfaces and local centers, and the shapes of cluster-shaped chaotic flows and invariant tori rely on the isosurfaces determined by initial conditions, while the numbers of clusters are subject to the local centers solved by the Hessian matrix of the Hamiltonian. Moreover, the study shows that the cluster-shaped chaotic flows and invariant tori are chained together by curve axes, which are the segments of equilibrium curves of the generalized thermostatted system. Furthermore, the interesting results are vividly demonstrated by the numerical simulations.

关键词: multiple equilibria, curve axes, invariant tori, cluster-shaped conservative chaos

Abstract: The thermostatted system is a conservative system different from Hamiltonian systems, and has attracted much attention because of its rich and different nonlinear dynamics. We report and analyze the multiple equilibria and curve axes of the cluster-shaped conservative flows generated from a generalized thermostatted system. It is found that the cluster-shaped structure is reflected in the geometry of the Hamiltonian, such as isosurfaces and local centers, and the shapes of cluster-shaped chaotic flows and invariant tori rely on the isosurfaces determined by initial conditions, while the numbers of clusters are subject to the local centers solved by the Hessian matrix of the Hamiltonian. Moreover, the study shows that the cluster-shaped chaotic flows and invariant tori are chained together by curve axes, which are the segments of equilibrium curves of the generalized thermostatted system. Furthermore, the interesting results are vividly demonstrated by the numerical simulations.

Key words: multiple equilibria, curve axes, invariant tori, cluster-shaped conservative chaos

中图分类号:  (Nonlinear dynamics and chaos)

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