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Basins of attraction for a quadratic coquaternionic map

Author

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  • Falcão, M. Irene
  • Miranda, Fernando
  • Severino, Ricardo
  • Soares, M. Joana

Abstract

In this paper we consider the extension, to the algebra of coquaternions, of a complex quadratic map with a real super-attractive 8-cycle. We establish that, in addition to the real cycle, this new map has sets of non-isolated periodic points of period 8, forming four attractive 8-cycles. Here, the cycles are to be interpreted as cycles of sets and an appropriate notion of attractivity is used. Some characteristics of the basins of attraction of the five attracting 8-cycles are discussed and plots revealing the intertwined nature of these basins are shown.

Suggested Citation

  • Falcão, M. Irene & Miranda, Fernando & Severino, Ricardo & Soares, M. Joana, 2017. "Basins of attraction for a quadratic coquaternionic map," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 716-724.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:716-724
    DOI: 10.1016/j.chaos.2017.09.016
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    References listed on IDEAS

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    1. Ata, Erhan & Yayli, Yusuf, 2009. "Split quaternions and semi-Euclidean projective spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1910-1915.
    2. Lakner, Mitja & Škapin-Rugelj, Marjeta & Petek, Peter, 2005. "Symbolic dynamics in investigation of quaternionic Julia sets," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1189-1201.
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    Cited by:

    1. Cui, Li & Luo, Wenhui & Ou, Qingli, 2021. "Analysis of basins of attraction of new coupled hidden attractor system," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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