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Hopf bifurcation analysis of a tabu learning two-neuron model

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  • Li, Yi
  • Zhou, Xiaobing
  • Wu, Yue
  • Zhou, Mingtian

Abstract

Tabu learning neural network applies the concept of tabu search to neural networks for solving optimization problems. In this paper, we study the nonlinear dynamical behaviors of a tabu learning two-neuron model with linear proximity function. By choosing the memory decay rate as the bifurcation parameter, we prove that Hopf bifurcation occurs in the model. The stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory. A numerical example is also presented to verify the theoretical analysis.

Suggested Citation

  • Li, Yi & Zhou, Xiaobing & Wu, Yue & Zhou, Mingtian, 2006. "Hopf bifurcation analysis of a tabu learning two-neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 190-197.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:1:p:190-197
    DOI: 10.1016/j.chaos.2005.08.016
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    References listed on IDEAS

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    1. Fred Glover, 1989. "Tabu Search---Part I," INFORMS Journal on Computing, INFORMS, vol. 1(3), pages 190-206, August.
    2. Chunguang Li & Guangrong Chen & Xiaofeng Liao & Juebang Yu, 2004. "Hopf bifurcation and chaos in a single inertial neuron model with time delay," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(3), pages 337-343, October.
    3. Fred Glover, 1990. "Tabu Search—Part II," INFORMS Journal on Computing, INFORMS, vol. 2(1), pages 4-32, February.
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    Cited by:

    1. Niu, Ben & Wei, Junjie, 2008. "Stability and bifurcation analysis in an amplitude equation with delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1362-1371.

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