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A new class of locally Hamiltonian conservative chaotic systems with the controlled multi-scrolls

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  • Jia, Hongyan
  • Wang, Hejin
  • Yu, Haibo
  • Han, Xiaoguang

Abstract

The paper first reports a new class of locally Hamiltonian conservative chaotic systems (CCSs) with the controlled multi-scrolls by using a piecewise function to replace the smooth Hamiltonian function. The novelty of the new locally Hamiltonian CCSs is that the Hamiltonian energy of each constituent system is locally conserved, and the conservation is related to the piecewise function and initial values. Besides, multi-scroll dynamics of them can also be controlled by adjusting the piecewise function. Subsequently, two cases are given to further show how to generate multi-scroll chaotic flows, and the corresponding Hamiltonian energy is also given to show their local conservation. Finally, the new locally Hamiltonian CCSs are implemented by using the Field-Programmable Gate Array (FPGA) technology, which not only physically show multi-scroll dynamics of them, but also provide the new pseudo-random signal generators for chaos applications.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:197:y:2025:i:c:s0960077925005181
    DOI: 10.1016/j.chaos.2025.116505
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    References listed on IDEAS

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    1. 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.
    2. Zhang, Xiaohong & Xu, Jingjing & Moshayedi, Ata Jahangir, 2024. "Design and FPGA implementation of a hyperchaotic conservative circuit with initial offset-boosting and transient transition behavior based on memcapacitor," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
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    4. Mathale, D. & Doungmo Goufo, Emile F. & Khumalo, M., 2020. "Coexistence of multi-scroll chaotic attractors for fractional systems with exponential law and non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 139(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. Soliman, Nancy S. & Tolba, Mohammed F. & Said, Lobna A. & Madian, Ahmed H. & Radwan, Ahmed G., 2019. "Fractional X-shape controllable multi-scroll attractor with parameter effect and FPGA automatic design tool software," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 292-307.
    7. 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).
    8. Dong, Qing & Zhou, Shihua & Zhang, Qiang & Kasabov, Nikola K., 2023. "A new five-dimensional non-Hamiltonian conservative hyperchaos system with multistability and transient properties," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    9. 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).
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