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Bifurcation analysis for a discrete-time Hopfield neural network of two neurons with two delays and self-connections

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  • Kaslik, E.
  • Balint, St.

Abstract

In this paper, a bifurcation analysis is undertaken for a discrete-time Hopfield neural network of two neurons with two different delays and self-connections. Conditions ensuring the asymptotic stability of the null solution are found, with respect to two characteristic parameters of the system. It is shown that for certain values of these parameters, Fold or Neimark-Sacker bifurcations occur, but Flip and codimension 2 (Fold–Neimark-Sacker, double Neimark-Sacker, resonance 1:1 and Flip–Neimark-Sacker) bifurcations may also be present. The direction and the stability of the Neimark-Sacker bifurcations are investigated by applying the center manifold theorem and the normal form theory.

Suggested Citation

  • Kaslik, E. & Balint, St., 2009. "Bifurcation analysis for a discrete-time Hopfield neural network of two neurons with two delays and self-connections," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 83-91.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:1:p:83-91
    DOI: 10.1016/j.chaos.2007.01.126
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    References listed on IDEAS

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    1. Zhang, Chunrui & Zheng, Baodong, 2005. "Hopf bifurcation in numerical approximation of a n-dimension neural network model with multi-delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 129-146.
    2. Kaslik, E. & Balint, St., 2007. "Bifurcation analysis for a two-dimensional delayed discrete-time Hopfield neural network," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1245-1253.
    3. Zhang, Chunrui & Zheng, Baodong, 2007. "Stability and bifurcation of a two-dimension discrete neural network model with multi-delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1232-1242.
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    Cited by:

    1. Wan, Li & Zhou, Qinghua & Liu, Jie, 2017. "Delay-dependent attractor analysis of Hopfield neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 68-72.

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