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A hyperchaos generated from Lorenz system

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  • Wang, Xingyuan
  • Wang, Mingjun

Abstract

This paper presents a four-dimension hyperchaotic Lorenz system, obtained by adding a nonlinear controller to Lorenz chaotic system. The hyperchaotic Lorenz system is studied by bifurcation diagram, Lyapunov exponents spectrum and phase diagram. Numerical simulations show that the new system’s behavior can be convergent, divergent, periodic, chaotic and hyperchaotic when the parameter varies.

Suggested Citation

  • Wang, Xingyuan & Wang, Mingjun, 2008. "A hyperchaos generated from Lorenz system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3751-3758.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:14:p:3751-3758
    DOI: 10.1016/j.physa.2008.02.020
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    References listed on IDEAS

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    1. Zhang, Hao & Ma, Xi-kui & Li, Ming & Zou, Jian-long, 2005. "Controlling and tracking hyperchaotic Rössler system via active backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 353-361.
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    Cited by:

    1. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Zhou, Shuang & Wang, Xingyuan, 2020. "Simple estimation method for the second-largest Lyapunov exponent of chaotic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Yu, Mengyao & Sun, Kehui & Liu, Wenhao & He, Shaobo, 2018. "A hyperchaotic map with grid sinusoidal cavity," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 107-117.
    4. Li, Ming & Wang, Mengdie & Fan, Haiju & An, Kang & Liu, Guoqi, 2022. "A novel plaintext-related chaotic image encryption scheme with no additional plaintext information," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    5. Fuchen Zhang & Rui Chen & Xiusu Chen, 2017. "Analysis of a Generalized Lorenz–Stenflo Equation," Complexity, Hindawi, vol. 2017, pages 1-6, December.
    6. Xiaofei Zhou & Junmei Li & Yulan Wang & Wei Zhang, 2019. "Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method," Complexity, Hindawi, vol. 2019, pages 1-13, February.
    7. Shunjie Li & Yawen Wu & Xuebing Zhang, 2021. "Analysis and Synchronization of a New Hyperchaotic System with Exponential Term," Mathematics, MDPI, vol. 9(24), pages 1-16, December.
    8. Zhang, Fuchen & Shu, Yonglu, 2015. "Global dynamics for the simplified Lorenz system model," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 53-60.
    9. María Pilar Mareca & Borja Bordel, 2017. "Improving the Complexity of the Lorenz Dynamics," Complexity, Hindawi, vol. 2017, pages 1-16, January.
    10. Peng, Xuenan & Zeng, Yicheng, 2020. "Image encryption application in a system for compounding self-excited and hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    11. Fuchen Zhang, 2019. "Analysis of a Lorenz-Like Chaotic System by Lyapunov Functions," Complexity, Hindawi, vol. 2019, pages 1-6, July.
    12. Fuchen Zhang & Min Xiao, 2019. "Complex Dynamical Behaviors of Lorenz-Stenflo Equations," Mathematics, MDPI, vol. 7(6), pages 1-9, June.
    13. Liu, Hongjun & Zhang, Yingqian & Kadir, Abdurahman & Xu, Yanqiu, 2019. "Image encryption using complex hyper chaotic system by injecting impulse into parameters," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 83-93.
    14. Fan, Chunlei & Ding, Qun, 2022. "A universal method for constructing non-degenerate hyperchaotic systems with any desired number of positive Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    15. Ojoniyi, Olurotimi S. & Njah, Abdulahi N., 2016. "A 5D hyperchaotic Sprott B system with coexisting hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 172-181.

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