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A novel amplitude control method for constructing nested hidden multi-butterfly and multiscroll chaotic attractors

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  • Wu, Qiujie
  • Hong, Qinghui
  • Liu, Xiaoyang
  • Wang, Xiaoping
  • Zeng, Zhigang

Abstract

A novel amplitude control method (ACM) is proposed to construct multiple self-excited or hidden attractors by scaling partial or total variables without changing their dynamic and topological properties. Various attractors including nested attractor, axisymmetric attractor, and centrosymmetric attractor can be obtained by multiplying signals with different amplitudes. An universal pulse control module is designed to realize the amplitude scale. Different number of scrolls can be adjusted by regulating the pulse signals without redesigning the nonlinear circuit. The classical Lorenz system and Jerk system are employed as examples to generate nested hidden multi-butterfly and multiscroll attractors. Some novel properties of ACM, such as nested morphology, amplitude modulation, and constant Lyapunov exponential spectrum, are analyzed theoretically and simulated numerically. The circuit design and PSpice simulation results are implemented to verify the availability and feasibility of the proposed approach.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301296
    DOI: 10.1016/j.chaos.2020.109727
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    References listed on IDEAS

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    1. 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.
    2. Sprott, J.C. & Munmuangsaen, Buncha, 2018. "Comment on “A hidden chaotic attractor in the classical Lorenz system”," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 261-262.
    3. Munmuangsaen, Buncha & Srisuchinwong, Banlue, 2018. "A hidden chaotic attractor in the classical Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 61-66.
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    Cited by:

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    2. Azam, Anam & Aqeel, Muhammad & Sunny, Danish Ali, 2022. "Generation of Multidirectional Mirror Symmetric Multiscroll Chaotic Attractors (MSMCA) in Double Wing Satellite Chaotic System," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Yan, Minxiu & Jie, Jingfeng, 2022. "Fractional-order multiwing switchable chaotic system with a wide range of parameters," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Sahoo, Shilalipi & Roy, Binoy Krishna, 2022. "A new multi-wing chaotic attractor with unusual variation in the number of wings," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Lin, Hairong & Wang, Chunhua & Du, Sichun & Yao, Wei & Sun, Yichuang, 2023. "A family of memristive multibutterfly chaotic systems with multidirectional initial-based offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Peng, Hongxin & Ji’e, Musha & Du, Xinyu & Duan, Shukai & Wang, Lidan, 2023. "Design of pseudorandom number generator based on a controllable multi-double-scroll chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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