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Bifurcation analysis and linear control of the Newton–Leipnik system

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  • Wang, Xuedi
  • Tian, Lixin

Abstract

In this paper, we study a sort of chaotic system—Newton–Leipnik system which possesses two strange attractors. The static and dynamic bifurcations of the system are studied. The chaos controlling is performed by a simpler linear controller, and numerical simulation of the control is supplied. At the same time, Lyapunov exponents of the system show that the result of the chaos controlling is right.

Suggested Citation

  • Wang, Xuedi & Tian, Lixin, 2006. "Bifurcation analysis and linear control of the Newton–Leipnik system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 31-38.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:1:p:31-38
    DOI: 10.1016/j.chaos.2005.04.009
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    Cited by:

    1. Lv, Jian Cheng & Yi, Zhang, 2007. "Stability and chaos of LMSER PCA learning algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1440-1447.
    2. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou & Chen, Wen-Chin & Lin, Kuang-Tai & Kang, Yuan, 2008. "Chaos in the Newton–Leipnik system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 98-103.
    3. Lv, Jian Cheng & Yi, Zhang, 2007. "Some chaotic behaviors in a MCA learning algorithm with a constant learning rate," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1040-1047.
    4. Barakat, Elsayed & Abdel-Aty, M. & El-Kalla, I.L., 2021. "Hyperchaotic and quasiperiodic behaviors of a two-photon laser with multi-intermediate states," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Jia, Qiang, 2008. "Chaos control and synchronization of the Newton–Leipnik chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 814-824.

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