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Infinite lattice of hyperchaotic strange attractors

Author

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  • Li, Chunbiao
  • Sprott, Julien Clinton
  • Kapitaniak, Tomasz
  • Lu, Tianai

Abstract

By introducing trigonometric functions in a 4-D hyperchaotic snap system, infinite 1-D, 2-D, and 3-D lattices of hyperchaotic strange attractors were produced. Furthermore a general approach was developed for constructing self-reproducing systems, in which infinitely many attractors share the same Lyapunov exponents. In this case, cumbersome constants are necessary to obtain offset boosting; correspondingly additional periodic functions are needed for attractor hatching. As an example, a hyperchaotic system with a hidden attractor was transformed for reproducing 1-D, 2-D infinite lattices of hyperchaotic attractors and a 4-D lattice of chaotic attractors.

Suggested Citation

  • Li, Chunbiao & Sprott, Julien Clinton & Kapitaniak, Tomasz & Lu, Tianai, 2018. "Infinite lattice of hyperchaotic strange attractors," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 76-82.
    • Handle: RePEc:eee:chsofr:v:109:y:2018:i:c:p:76-82
    DOI: 10.1016/j.chaos.2018.02.022
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    Cited by:

    1. Zhou, Ling & You, Zhenzhen & Tang, Yun, 2021. "A new chaotic system with nested coexisting multiple attractors and riddled basins," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Li, Chunbiao & Gu, Zhenyu & Liu, Zuohua & Jafari, Sajad & Kapitaniak, Tomasz, 2021. "Constructing chaotic repellors," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Leutcho, Gervais Dolvis & Kengne, Jacques, 2018. "A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 275-293.
    4. Wu, Qiujie & Hong, Qinghui & Liu, Xiaoyang & Wang, Xiaoping & Zeng, Zhigang, 2020. "A novel amplitude control method for constructing nested hidden multi-butterfly and multiscroll chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Wei, Zhouchao & Zhu, Bin & Yang, Jing & Perc, Matjaž & Slavinec, Mitja, 2019. "Bifurcation analysis of two disc dynamos with viscous friction and multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 265-281.
    6. Gu, Shuangquan & He, Shaobo & Wang, Huihai & Du, Baoxiang, 2021. "Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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