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Hopf bifurcation in numerical approximation of a n-dimension neural network model with multi-delays

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  • Zhang, Chunrui
  • Zheng, Baodong

Abstract

In this paper we consider the numerical approximation of a n-dimension neural network model with multi-delays undergoing a Hopf bifurcation. We prove that if the neural network model has a Hopf bifurcation point at τ=τ∗, then the discrete neural network model obtained by Euler-method also has a Hopf bifurcation point at τh=τ∗+O(h).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:1:p:129-146
    DOI: 10.1016/j.chaos.2004.09.099
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    Citations

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    Cited by:

    1. 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.
    2. Li, Fengjun & Xu, Zongben, 2008. "The estimation of simultaneous approximation order for neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 572-580.
    3. Yang, Xiaofan & Yang, Maobin & Liu, Huaiyi & Liao, Xiaofeng, 2008. "Bautin bifurcation in a class of two-neuron networks with resonant bilinear terms," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 575-589.
    4. 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.
    5. 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.
    6. Yang, Yu & Ye, Jin, 2009. "Stability and bifurcation in a simplified five-neuron BAM neural network with delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2357-2363.
    7. Wang, Hongbin & Jiang, Weihua, 2006. "Multiple stabilities analysis in a magnetic bearing system with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 789-799.
    8. Zheng, Baodong & Zhang, Yang & Zhang, Chunrui, 2008. "Stability and bifurcation of a discrete BAM neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 612-616.
    9. Zhang, Chunrui & Zu, Yuangang & Zheng, Baodong, 2006. "Stability and bifurcation of a discrete red blood cell survival model," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 386-394.

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