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Energy analysis of Sprott-A system and generation of a new Hamiltonian conservative chaotic system with coexisting hidden attractors

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  • Jia, Hongyan
  • Shi, Wenxin
  • Wang, Lei
  • Qi, Guoyuan

Abstract

The paper firstly investigates energy cycle of the Sprott-A system by transforming the Sprott-A system into the Kolmogorov-type system. We found the dynamics of the Sprott-A system are influenced by the change along the energy exchange between the conservative energy and the external supplied energy. And the action of the external supplied torque is the main reason that the Sprott-A system generates chaos. Secondly, based on energy analysis of the Sprott-A system, a new four-dimension (4-D) chaotic system is obtained. The new 4-D chaotic system is a conservative system with a constant Hamiltonian energy. Besides, it is also a no-equilibrium system, this means that the new 4-D chaotic system can exhibit hidden characteristics. Further, the coexisting hidden attractors are found when selecting different initial points. Finally, the new 4-D chaotic system is implemented by FPGA, and the coexisting attractors observed are consistent with those found in numerical analysis, which in experiment verifies the existence of coexisting hidden attractors of the new 4-D chaotic system from physical point of view.

Suggested Citation

  • Jia, Hongyan & Shi, Wenxin & Wang, Lei & Qi, Guoyuan, 2020. "Energy analysis of Sprott-A system and generation of a new Hamiltonian conservative chaotic system with coexisting hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300345
    DOI: 10.1016/j.chaos.2020.109635
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    References listed on IDEAS

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    1. Bao, B.C. & Bao, H. & Wang, N. & Chen, M. & Xu, Q., 2017. "Hidden extreme multistability in memristive hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 102-111.
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    6. Singh, Jay Prakash & Roy, Binoy Krishna, 2018. "Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 81-91.
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    Cited by:

    1. Yu, Hui & Du, Shengzhi & Dong, Enzeng & Tong, Jigang, 2022. "Transient behaviors and equilibria-analysis-based boundary crisis analysis in a smooth 4D dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Leng, Xiangxin & Gu, Shuangquan & Peng, Qiqi & Du, Baoxiang, 2021. "Study on a four-dimensional fractional-order system with dissipative and conservative properties," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Zhang, Zefeng & Huang, Lilian & Liu, Jin & Guo, Qiang & Du, Xiuli, 2022. "A new method of constructing cyclic symmetric conservative chaotic systems and improved offset boosting control," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    4. Liu, Tianming & Yan, Huizhen & Banerjee, Santo & Mou, Jun, 2021. "A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. 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).
    6. Vijayakumar, M.D. & Natiq, Hayder & Tametang Meli, Maxim Idriss & Leutcho, Gervais Dolvis & Tabekoueng Njitacke, Zeric, 2022. "Hamiltonian energy computation of a novel memristive mega-stable oscillator (MMO) with dissipative, conservative and repelled dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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