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On a 3-D generalized Hamiltonian model with conservative and dissipative chaotic flows

Author

Listed:
  • Cang, Shijian
  • Wu, Aiguo
  • Wang, Zenghui
  • Chen, Zengqiang

Abstract

Based on the generalized Hamiltonian system, a new method for constructing a class of three-dimensional (3-D) chaotic systems is presented in this paper. After choosing the proper parameters of skew-symmetric matrix, dissipative matrix and external input, one smooth 3-D chaotic system is proposed to show the effectiveness of the proposed method. Numerical simulation techniques, including phase portraits, Poincaré sections, Lyapunov exponents and bifurcation diagram, illustrate that the proposed 3-D system has periodic, quasi-periodic and chaotic flows under the conditions of different parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:99:y:2017:i:c:p:45-51
    DOI: 10.1016/j.chaos.2017.03.046
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    References listed on IDEAS

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    1. Shijian Cang & Zenghui Wang & Zengqiang Chen, 2013. "Adaptive Sliding Mode Controller Design for Projective Synchronization of Different Chaotic Systems with Uncertain Terms and External Bounded Disturbances," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, July.
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    Cited by:

    1. Ma, Zhiyao & Sun, Ke & Tong, Shaocheng, 2024. "Adaptive asymptotic tracking control of uncertain fractional-order nonlinear systems with unknown control coefficients and actuator faults," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. 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).
    3. 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).
    4. Wu, Fuqiang & Zhou, Ping & Alsaedi, Ahmed & Hayat, Tasawar & Ma, Jun, 2018. "Synchronization dependence on initial setting of chaotic systems without equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 124-132.
    5. Liu, Xilin & Tong, Xiaojun & Wang, Zhu & Zhang, Miao, 2022. "A new n-dimensional conservative chaos based on Generalized Hamiltonian System and its’ applications in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    6. Wu, Xin & Shi, Hang & Ji’e, Musha & Duan, Shukai & Wang, Lidan, 2023. "A novel image compression and encryption scheme based on conservative chaotic system and DNA method," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    7. Zhou, Ping & Hu, Xikui & Zhu, Zhigang & Ma, Jun, 2021. "What is the most suitable Lyapunov function?," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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