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When Darwin meets Lorenz: Evolving new chaotic attractors through genetic programming

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  • Pan, Indranil
  • Das, Saptarshi

Abstract

In this paper, we propose a novel methodology for automatically finding new chaotic attractors through a computational intelligence technique known as multi-gene genetic programming (MGGP). We apply this technique to the case of the Lorenz attractor and evolve several new chaotic attractors based on the basic Lorenz template. The MGGP algorithm automatically finds new nonlinear expressions for the different state variables starting from the original Lorenz system. The Lyapunov exponents of each of the attractors are calculated numerically based on the time series of the state variables using time delay embedding techniques. The MGGP algorithm tries to search the functional space of the attractors by aiming to maximise the largest Lyapunov exponent (LLE) of the evolved attractors. To demonstrate the potential of the proposed methodology, we report over one hundred new chaotic attractor structures along with their parameters, which are evolved from just the Lorenz system alone.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:76:y:2015:i:c:p:141-155
    DOI: 10.1016/j.chaos.2015.03.017
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    References listed on IDEAS

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    1. Ian Stewart, 2000. "The Lorenz attractor exists," Nature, Nature, vol. 406(6799), pages 948-949, August.
    2. Ping Zhou & Kun Huang & Chun-de Yang, 2013. "A Fractional-Order Chaotic System with an Infinite Number of Equilibrium Points," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-6, April.
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    Cited by:

    1. Wang, Haijun & Li, Xianyi, 2018. "A novel hyperchaotic system with infinitely many heteroclinic orbits coined," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 5-15.
    2. Pham, Viet–Thanh & Jafari, Sajad & Volos, Christos & Kapitaniak, Tomasz, 2016. "A gallery of chaotic systems with an infinite number of equilibrium points," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 58-63.

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