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The Lorenz attractor exists

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  • Ian Stewart

    (Mathematics Institute, University of Warwick)

Abstract

The Lorenz attractor is an example of deterministic chaos. Previously, the Lorenz attractor could only be generated by numerical approximations on a computer. Now we have a rigorous proof that confirms its existence.

Suggested Citation

  • Ian Stewart, 2000. "The Lorenz attractor exists," Nature, Nature, vol. 406(6799), pages 948-949, August.
    • Handle: RePEc:nat:nature:v:406:y:2000:i:6799:d:10.1038_35023206
    DOI: 10.1038/35023206
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    Citations

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    Cited by:

    1. Wu, Xiaoqun & Lu, Jun-an & Tse, Chi K. & Wang, Jinjun & Liu, Jie, 2007. "Impulsive control and synchronization of the Lorenz systems family," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 631-638.
    2. Pooriya Beyhaghi & Ryan Alimo & Thomas Bewley, 2020. "A derivative-free optimization algorithm for the efficient minimization of functions obtained via statistical averaging," Computational Optimization and Applications, Springer, vol. 76(1), pages 1-31, May.
    3. Boeing, Geoff, 2017. "Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction," SocArXiv c7p43, Center for Open Science.
    4. Wang, Junwei & Zhao, Meichun & Zhang, Yanbin & Xiong, Xiaohua, 2007. "S˘i’lnikov-type orbits of Lorenz-family systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 438-446.
    5. Stephen Thompson, 2022. "“The total movement of this disorder is its order”: Investment and utilization dynamics in long‐run disequilibrium," Metroeconomica, Wiley Blackwell, vol. 73(2), pages 638-682, May.
    6. Pan, Indranil & Das, Saptarshi, 2015. "When Darwin meets Lorenz: Evolving new chaotic attractors through genetic programming," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 141-155.
    7. Kavuran, Gürkan, 2022. "When machine learning meets fractional-order chaotic signals: detecting dynamical variations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    8. Yassen, M.T., 2005. "Feedback and adaptive synchronization of chaotic Lü system," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 379-386.
    9. Yassen, M.T., 2006. "Chaos control of chaotic dynamical systems using backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 537-548.
    10. Boeing, Geoff, 2017. "Methods and Measures for Analyzing Complex Street Networks and Urban Form," SocArXiv 93h82, Center for Open Science.
    11. dos Santos, Vagner & Szezech Jr., José D. & Baptista, Murilo S. & Batista, Antonio M. & Caldas, Iberê L., 2016. "Unstable dimension variability structure in the parameter space of coupled Hénon maps," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 23-28.

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