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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 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 |
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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.
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Received: 13 April 2021
Revised: 18 May 2021
Accepted manuscript online: 11 June 2021
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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| Fund: 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. |
Corresponding Authors:
Shijian Cang
E-mail: sj.cang@gmail.com
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Cite this article:
Yue Li(李月), Zengqiang Chen(陈增强), Zenghui Wang(王增会), and Shijian Cang(仓诗建) Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system 2022 Chin. Phys. B 31 010501
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