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Existence of a new three-dimensional chaotic attractor

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  • Wang, Jiezhi
  • Chen, Zengqiang
  • Yuan, Zhuzhi

Abstract

In this paper, one heteroclinic orbit of a new three-dimensional continuous autonomous chaotic system, whose chaotic attractor belongs to the conjugate Lü attractor, is found. The series expression of the heteroclinic orbit of Šhil’nikov type is derived by using the undetermined coefficient method. The uniform convergence of the precise series expansions of this heteroclinic orbits is proved. According to the Šhil’nikov theorem, this system clearly has Smale horseshoes and the horseshoe chaos.

Suggested Citation

  • Wang, Jiezhi & Chen, Zengqiang & Yuan, Zhuzhi, 2009. "Existence of a new three-dimensional chaotic attractor," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3053-3057.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:3053-3057
    DOI: 10.1016/j.chaos.2009.04.011
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    References listed on IDEAS

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    1. Čelikovský, Sergej & Chen, Guanrong, 2005. "On the generalized Lorenz canonical form," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1271-1276.
    2. 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.
    3. Wu, Xiaoqun & Lu, Jun-an & Iu, Herbert H.C. & Wong, Siu-Chung, 2007. "Suppression and generation of chaos for a three-dimensional autonomous system using parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 811-819.
    4. Chen, Zengqiang & Yang, Yong & Yuan, Zhuzhi, 2008. "A single three-wing or four-wing chaotic attractor generated from a three-dimensional smooth quadratic autonomous system," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1187-1196.
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    Cited by:

    1. Giovanni Bella, 2017. "Beyond the Accelerating Inflation Controversy: The Jerk and Jounce Price Variation," International Journal of Economics and Financial Research, Academic Research Publishing Group, vol. 3(11), pages 315-322, 11-2017.

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