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Energy cycle for the Lorenz attractor

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  • Pelino, Vinicio
  • Maimone, Filippo
  • Pasini, Antonello

Abstract

In this paper we identify an energetic cycle in the Lorenz-63 system through its Lie–Poisson structure. A new geometrical view of this Lorenz system is presented and sheds light on its energetic properties by recovering its Hamiltonian structure and the associated Casimir. It is shown that this approach gives notable physical insight on the dynamical behaviour of the system. A link between energetics and chaotic properties has been found and specific inequalities, involving conversion terms, have been identified. Traps and jumps between the lobes are studied and benefits of our formalism to capture predictability-energy connections are discussed.

Suggested Citation

  • Pelino, Vinicio & Maimone, Filippo & Pasini, Antonello, 2014. "Energy cycle for the Lorenz attractor," Chaos, Solitons & Fractals, Elsevier, vol. 64(C), pages 67-77.
    • Handle: RePEc:eee:chsofr:v:64:y:2014:i:c:p:67-77
    DOI: 10.1016/j.chaos.2013.09.005
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    Cited by:

    1. Yang, Yingjuan & Qi, Guoyuan, 2018. "Mechanical analysis and bound of plasma chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 187-195.
    2. Yang, Shuangling & Qu, Jingjia, 2021. "On first integrals of a family of generalized Lorenz-like systems," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. 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.
    4. 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).
    5. Qi, Guoyuan & Zhang, Jiangfeng, 2017. "Energy cycle and bound of Qi chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 7-15.
    6. Guoyuan Qi & Xiaogang Yang, 2019. "Modeling of a Chaotic Gyrostat System and Mechanism Analysis of Dynamics Using Force and Energy," Complexity, Hindawi, vol. 2019, pages 1-13, July.
    7. Alexander Gluhovsky, 2017. "A Gyrostatic Low-Order Model for the El Ñino-Southern Oscillation," Complexity, Hindawi, vol. 2017, pages 1-4, January.

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