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Multi-wing hyperchaotic attractors from coupled Lorenz systems

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  • Grassi, Giuseppe
  • Severance, Frank L.
  • Miller, Damon A.

Abstract

This paper illustrates an approach to generate multi-wing attractors in coupled Lorenz systems. In particular, novel four-wing (eight-wing) hyperchaotic attractors are generated by coupling two (three) identical Lorenz systems. The paper shows that the equilibria of the proposed systems have certain symmetries with respect to specific coordinate planes and the eigenvalues of the associated Jacobian matrices exhibit the property of similarity. In analogy with the original Lorenz system, where the two-wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four-wings (eight-wings) of these attractors are located around the four (eight) equilibria with two (three) pairs of unstable complex-conjugate eigenvalues.

Suggested Citation

  • Grassi, Giuseppe & Severance, Frank L. & Miller, Damon A., 2009. "Multi-wing hyperchaotic attractors from coupled Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 284-291.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:284-291
    DOI: 10.1016/j.chaos.2007.12.003
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    References listed on IDEAS

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    1. Chen, Qingfei & Hong, Yiguang & Chen, Guanrong, 2006. "Chaotic behaviors and toroidal/spherical attractors generated by discontinuous dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 293-302.
    2. Qi, Guoyuan & Du, Shengzhi & Chen, Guanrong & Chen, Zengqiang & yuan, Zhuzhi, 2005. "On a four-dimensional chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1671-1682.
    3. Ahmad, Wajdi M., 2005. "Generation and control of multi-scroll chaotic attractors in fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 727-735.
    4. Ahmad, Wajdi M., 2006. "A simple multi-scroll hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1213-1219.
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    Cited by:

    1. Aguirre-Hernández, B. & Campos-Cantón, E. & López-Renteria, J.A. & Díaz González, E.C., 2015. "A polynomial approach for generating a monoparametric family of chaotic attractors via switched linear systems," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 100-106.
    2. Cheng, Guanghui & Li, Dan & Yao, Yuangen & Gui, Rong, 2023. "Multi-scroll chaotic attractors with multi-wing via oscillatory potential wells," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Signing, V.R. Folifack & Kengne, J. & Kana, L.K., 2018. "Dynamic analysis and multistability of a novel four-wing chaotic system with smooth piecewise quadratic nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 263-274.
    4. Vivekanandhan, Gayathri & Chedjou, Jean Chamberlain & Jacques, Kengne & Rajagopal, Karthikeyan, 2024. "A unique self-driven 5D hyperjerk circuit with hyperbolic sine function: Hyperchaos with three positive exponents, complex transient behavior and coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).

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