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Generating multicluster conservative chaotic flows from a generalized Sprott-A system

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  • Cang, Shijian
  • Li, Yue
  • Kang, Zhijun
  • Wang, Zenghui

Abstract

In this paper, we propose a general structure of the generalized Sprott-A system based on the matrix form of the Sprott-A system. To investigate the multicluster chaotic flows derived from the general structure, several example systems are reported by modifying the Hamiltonian of the generalized Sprott-A system without changing its nonconstant state matrix. Through numerical simulations, it is interesting to find that the topology of the chaotic flows generated by the example systems has clusters of different numbers and shapes in phase space for the given different parameters and initial conditions, which are completely controlled by the Hamiltonian (i.e., completely closed isosurfaces). Moreover, the captured chaos is volume-conservative, which is verified by the sums of the corresponding Lyapunov exponents. Besides, we analyze the complexity of the example systems by the approximate entropy, sample entropy and fuzzy entropy, and find that increasing the number of conservative chaotic clusters may not enhance the complexities of the proposed systems.

Suggested Citation

  • Cang, Shijian & Li, Yue & Kang, Zhijun & Wang, Zenghui, 2020. "Generating multicluster conservative chaotic flows from a generalized Sprott-A system," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300503
    DOI: 10.1016/j.chaos.2020.109651
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    References listed on IDEAS

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    1. Zhonglin Wang & Shijian Cang & Zenghui Wang & Wei Xue & Zengqiang Chen, 2014. "A Strange Double-Deck Butterfly Chaotic Attractor from a Permanent Magnet Synchronous Motor with Smooth Air Gap: Numerical Analysis and Experimental Observation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, July.
    2. Cang, Shijian & Wu, Aiguo & Wang, Zenghui & Chen, Zengqiang, 2017. "On a 3-D generalized Hamiltonian model with conservative and dissipative chaotic flows," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 45-51.
    3. Gaspard, Pierre, 1997. "Chaos and hydrodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(1), pages 54-67.
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    Cited by:

    1. Cang, Shijian & Wang, Luo & Zhang, Yapeng & Wang, Zenghui & Chen, Zengqiang, 2022. "Bifurcation and chaos in a smooth 3D dynamical system extended from Nosé-Hoover oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Li, Yue & Yuan, Mingfeng & Chen, Zengqiang, 2022. "Multi-parameter analysis of transition from conservative to dissipative behaviors for a reversible dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Li, Yue & Yuan, Mingfeng & Chen, Zengqiang, 2023. "Constructing 3D conservative chaotic system with dissipative term based on Shilnikov theorem," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    4. Zeng, Jian & Ding, Qun, 2025. "New methods for constructing 2n / 2n+1-dimensional conservative chaotic systems and FPGA implementation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 674(C).
    5. Yao, Wenpo & Yao, Wenli & Wang, Jun, 2021. "A novel parameter for nonequilibrium analysis in reconstructed state spaces," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    6. Wang, Zhen & Ahmadi, Atefeh & Tian, Huaigu & Jafari, Sajad & Chen, Guanrong, 2023. "Lower-dimensional simple chaotic systems with spectacular features," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    7. Tong, Xiaojun & Liu, Xilin & Zhang, Miao & Wang, Zhu, 2024. "A high-quality visual image encryption algorithm utilizing the conservative chaotic system and adaptive embedding," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    8. Cang, Shijian & Zhao, Gehang & Wang, Zenghui & Chen, Zengqiang, 2022. "Global structures of clew-shaped conservative chaotic flows in a class of 3D one-thermostat systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    9. Pan, Hepeng & Li, Guodong & Xu, Wenxia & Zhang, Jingxu, 2025. "Construction, analysis and DSP implementation of Hamiltonian conservative chaotic system based on permutation group rotation multiplication method," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    10. Jia, Hongyan & Liu, Jingwen & Li, Wei & Du, Meng, 2023. "A family of new generalized multi-scroll Hamiltonian conservative chaotic flows on invariant hypersurfaces and FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    11. Jia, Hongyan & Wang, Hejin & Yu, Haibo & Han, Xiaoguang, 2025. "A new class of locally Hamiltonian conservative chaotic systems with the controlled multi-scrolls," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).

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