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Linear and rotational fractal design for multiwing hyperchaotic systems with triangle and square shapes

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  • Doungmo Goufo, Emile F.

Abstract

Since the German biochemist Otto Rössler proposed the first hyperchaotic model in the years 1970s and showed to the scientific community how important hyperchaos can be in describing real life phenomena, it has become necessary to develop and propose various techniques capable of generating hyperchaotic attractors with more complex dynamics applicable in both theory and practice. We propose in this paper, an innovative method with analytical and numerical aspects able to generate a class of hyperchaotic attractors with many wings and different shapes. We use a fractal operator to obtain an expression of the modified fractal-fractional Lü system, which is therefore solved numerically. After showing that the initial model is hyperchaotic, we perform some numerical simulations that prove that the hyperchaotic status of the system remain unchanged. The results show that the modified system can generate hyperchaotic attractors of types n-wings, n × m-wings, n × m × p-wings and n × m × p × r-wings (m, n, p, r ∈ ℕ), using both linear and rotational variations. It appears that the system is involved in fractal designs comprising a linear or rotational self-duplication process happening in different scales across the system and ending up with the triangular or square shape.

Suggested Citation

  • Doungmo Goufo, Emile F., 2022. "Linear and rotational fractal design for multiwing hyperchaotic systems with triangle and square shapes," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922004933
    DOI: 10.1016/j.chaos.2022.112283
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    References listed on IDEAS

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    1. 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.
    2. Naik, Parvaiz Ahmad & Owolabi, Kolade M. & Yavuz, Mehmet & Zu, Jian, 2020. "Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Chen, Aimin & Lu, Junan & Lü, Jinhu & Yu, Simin, 2006. "Generating hyperchaotic Lü attractor via state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 103-110.
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