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Mechanical analysis of Chen chaotic system

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  • Liang, Xiyin
  • Qi, Guoyuan

Abstract

The Chen chaotic system is transformed into Kolmogorov type system, which is decomposed into four types of torques: inertial torque, internal torque, dissipation and external torque. By the combinations of different torques, five cases are studied to discover key factors of chaos generation and the physical meaning. The conversion among Hamiltonian energy, kinetic energy and potential energy is investigated in these five cases. The relationship between the energies and the parameters is studied. It concludes that the combination of these four types of torques is necessary conditions to produce chaos, and any combination of three types of torques cannot produce chaos in Chen system.

Suggested Citation

  • Liang, Xiyin & Qi, Guoyuan, 2017. "Mechanical analysis of Chen chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 173-177.
    • Handle: RePEc:eee:chsofr:v:98:y:2017:i:c:p:173-177
    DOI: 10.1016/j.chaos.2017.03.021
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    References listed on IDEAS

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    1. Qi, Guoyuan & Chen, Guanrong & van Wyk, Michaël Antonie & van Wyk, Barend Jacobus & Zhang, Yuhui, 2008. "A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 705-721.
    2. Xu, Xu & Wiercigroch, M. & Cartmell, M.P., 2005. "Rotating orbits of a parametrically-excited pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1537-1548.
    3. Qi, Guoyuan & Chen, Guanrong & Du, Shengzhi & Chen, Zengqiang & Yuan, Zhuzhi, 2005. "Analysis of a new chaotic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 295-308.
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    Cited by:

    1. Yu, Hui & Du, Shengzhi & Dong, Enzeng & Tong, Jigang, 2022. "Transient behaviors and equilibria-analysis-based boundary crisis analysis in a smooth 4D dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Remus-Daniel Ene & Nicolina Pop, 2023. "Optimal Homotopy Asymptotic Method for an Anharmonic Oscillator: Application to the Chen System," Mathematics, MDPI, vol. 11(5), pages 1-14, February.
    3. Jia, Hongyan & Shi, Wenxin & Wang, Lei & Qi, Guoyuan, 2020. "Energy analysis of Sprott-A system and generation of a new Hamiltonian conservative chaotic system with coexisting hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    4. Yang, Yingjuan & Qi, Guoyuan, 2018. "Mechanical analysis and bound of plasma chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 187-195.
    5. Haiyun Bi & Guoyuan Qi & Jianbing Hu, 2019. "Modeling and Analysis of Chaos and Bifurcations for the Attitude System of a Quadrotor Unmanned Aerial Vehicle," Complexity, Hindawi, vol. 2019, pages 1-16, October.

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