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Global structures of clew-shaped conservative chaotic flows in a class of 3D one-thermostat systems

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  • Cang, Shijian
  • Zhao, Gehang
  • Wang, Zenghui
  • Chen, Zengqiang

Abstract

Inspired by the structure of the single-clew-shaped conservative chaotic flows generated from the Nosé–Hoover oscillator, the possible local dynamic behaviors of the thermostatted oscillator are discovered near the axis of the clew-shaped chaotic flows. Based on the formalism of the port-controlled Hamiltonian system, we propose a variant of the Nosé–Hoover oscillator, which denotes a class of 3D one-thermostat systems and satisfies the canonical probability distribution. Then, three example systems are constructed to demonstrate the global structures with one-, two- and eight-clew conservative chaotic flows. Numerical results show that the different global structures depend on both the system’s Hamiltonian that determines the basic shape of clew-shaped conservative chaotic flows and the curves of equilibrium points that contain the axis of each clew.

Suggested Citation

  • Cang, Shijian & Zhao, Gehang & Wang, Zenghui & Chen, Zengqiang, 2022. "Global structures of clew-shaped conservative chaotic flows in a class of 3D one-thermostat systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921010419
    DOI: 10.1016/j.chaos.2021.111687
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    References listed on IDEAS

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    1. Gandhimathi, V.M. & Murali, K. & Rajasekar, S., 2006. "Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1034-1047.
    2. Ahmad, Shabir & Ullah, Aman & Akgül, Ali, 2021. "Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Cui, Li & Lu, Ming & Ou, Qingli & Duan, Hao & Luo, Wenhui, 2020. "Analysis and Circuit Implementation of Fractional Order Multi-wing Hidden Attractors," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Cang, Shijian & Li, Yue & Kang, Zhijun & Wang, Zenghui, 2020. "Generating multicluster conservative chaotic flows from a generalized Sprott-A system," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
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    1. Wang, Zhen & Ahmadi, Atefeh & Tian, Huaigu & Jafari, Sajad & Chen, Guanrong, 2023. "Lower-dimensional simple chaotic systems with spectacular features," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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