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Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors

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  • Lai, Qiang
  • Norouzi, Benyamin
  • Liu, Feng

Abstract

This paper introduces an extended Lü system with coexisting attractors. The number and stability of equilibria are determined. The coexisting attractors of the system are displayed by the bifurcation diagrams, Lyapunov exponent spectrum, phase portraits. It is shown that the system has a pair of strange attractors, a pair of limit cycles, a pair of point attractors for different initial conditions. The circuit implementation of the chaotic attractor and coexisting attractors of the system are presented. The control problem of the system is studied as well. A controller is designed to stabilize the system to the origin and realize the switching between two chaotic attractors based on the passive control method. Moreover, a chaotic image encryption algorithm is proposed according to the system. The performance of the algorithm is numerically analyzed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:230-245
    DOI: 10.1016/j.chaos.2018.07.011
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    1. 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.
    2. Gao, Tiegang & Chen, Zengqiang & Gu, Qiaolun & Yuan, Zhuzhi, 2008. "A new hyper-chaos generated from generalized Lorenz system via nonlinear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 390-397.
    3. Pham, Viet–Thanh & Jafari, Sajad & Volos, Christos & Kapitaniak, Tomasz, 2016. "A gallery of chaotic systems with an infinite number of equilibrium points," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 58-63.
    4. Gao, Tiegang & Chen, Zengqiang, 2008. "Image encryption based on a new total shuffling algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 213-220.
    5. 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.
    6. Lai, Qiang & Nestor, Tsafack & Kengne, Jacques & Zhao, Xiao-Wen, 2018. "Coexisting attractors and circuit implementation of a new 4D chaotic system with two equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 92-102.
    7. Ertugrul M. Ozbudak & Mukund Thattai & Han N. Lim & Boris I. Shraiman & Alexander van Oudenaarden, 2004. "Multistability in the lactose utilization network of Escherichia coli," Nature, Nature, vol. 427(6976), pages 737-740, February.
    8. Nikolov, Svetoslav & Clodong, Sébastien, 2006. "Hyperchaos–chaos–hyperchaos transition in modified Rössler systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 252-263.
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