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Some chaotic behaviors in a MCA learning algorithm with a constant learning rate

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  • Lv, Jian Cheng
  • Yi, Zhang

Abstract

Douglas’s minor component analysis algorithm with a constant learning rate has both stability and chaotic dynamical behavior under some conditions. The paper explores such dynamical behavior of this algorithm. Certain stability and chaos of this algorithm are derived. Waveform plots, Lyapunov exponents and bifurcation diagrams are presented to illustrate the existence of chaotic behavior.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:3:p:1040-1047
    DOI: 10.1016/j.chaos.2006.01.064
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    References listed on IDEAS

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    1. He, Ji-Huan, 2005. "Limit cycle and bifurcation of nonlinear problems," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 827-833.
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    3. Cheng, Zunshui & Lin, Yiping & Cao, Jinde, 2006. "Dynamical behaviors of a partial-dependent predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 67-75.
    4. 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.
    5. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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