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Generating hyperchaotic Lü attractor via state feedback control

Author

Listed:
  • Chen, Aimin
  • Lu, Junan
  • Lü, Jinhu
  • Yu, Simin

Abstract

This paper constructs a new hyperchaotic system based on Lü system by using a state feedback controller. The detailed dynamical behaviors of this hyperchaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation, and Poincaré mapping. Moreover, a novel circuit diagram is designed for verifying the hyperchaotic behaviors and some experimental observations are also given.

Suggested Citation

  • Chen, Aimin & Lu, Junan & Lü, Jinhu & Yu, Simin, 2006. "Generating hyperchaotic Lü attractor via state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 103-110.
    • Handle: RePEc:eee:phsmap:v:364:y:2006:i:c:p:103-110
    DOI: 10.1016/j.physa.2005.09.039
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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. Yu, Yongguang & Li, Han-Xiong, 2009. "Application of the multistage homotopy-perturbation method to solve a class of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2330-2337.
    3. Wang, Haijun & Dong, Guili, 2019. "New dynamics coined in a 4-D quadratic autonomous hyper-chaotic system," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 272-286.
    4. Zhao, Junchan & Lu, Jun-an, 2008. "Using sampled-data feedback control and linear feedback synchronization in a new hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 376-382.
    5. Yassen, M.T., 2008. "Synchronization hyperchaos of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 465-475.
    6. Wang, Guangyi & Zhang, Xun & Zheng, Yan & Li, Yuxia, 2006. "A new modified hyperchaotic Lü system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 260-272.
    7. Lai, Qiang & Norouzi, Benyamin & Liu, Feng, 2018. "Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 230-245.
    8. Wu, Wenjuan & Chen, Zengqiang & Yuan, Zhuzhi, 2009. "The evolution of a novel four-dimensional autonomous system: Among 3-torus, limit cycle, 2-torus, chaos and hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2340-2356.
    9. 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).
    10. Zhou, Xiaobing & Wu, Yue & Li, Yi & Xue, Hongquan, 2009. "Adaptive control and synchronization of a new modified hyperchaotic Lü system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2477-2483.
    11. Jahanshahi, Hadi & Yousefpour, Amin & Wei, Zhouchao & Alcaraz, Raúl & Bekiros, Stelios, 2019. "A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 66-77.
    12. Xie, Qian & Si, Gangquan & Zhang, Yanbin & Yuan, Yiwei & Yao, Rui, 2016. "Finite-time synchronization and identification of complex delayed networks with Markovian jumping parameters and stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 35-49.
    13. 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.
    14. Doungmo Goufo, Emile F., 2022. "Linear and rotational fractal design for multiwing hyperchaotic systems with triangle and square shapes," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    15. Chen, Liping & Pan, Wei & Wang, Kunpeng & Wu, Ranchao & Machado, J. A. Tenreiro & Lopes, António M., 2017. "Generation of a family of fractional order hyper-chaotic multi-scroll attractors," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 244-255.
    16. Yu Feng & Zhouchao Wei & Uğur Erkin Kocamaz & Akif Akgül & Irene Moroz, 2017. "Synchronization and Electronic Circuit Application of Hidden Hyperchaos in a Four-Dimensional Self-Exciting Homopolar Disc Dynamo without Equilibria," Complexity, Hindawi, vol. 2017, pages 1-11, May.
    17. Tchitnga, R. & Mezatio, B.A. & Fozin, T. Fonzin & Kengne, R. & Louodop Fotso, P.H. & Fomethe, A., 2019. "A novel hyperchaotic three-component oscillator operating at high frequency," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 166-180.
    18. Yang, Zhen & Liu, Yinzhe & Wu, Yuqi & Qi, Yunliang & Ren, Fengyuan & Li, Shouliang, 2023. "A high speed pseudo-random bit generator driven by 2D-discrete hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    19. 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).
    20. 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.
    21. Natiq, Hayder & Banerjee, Santo & Misra, A.P. & Said, M.R.M., 2019. "Degenerating the butterfly attractor in a plasma perturbation model using nonlinear controllers," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 58-68.

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