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Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays

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  • Xiang-Ping Yan
  • Wan-Tong Li

Abstract

We first study the distribution of the zeros of a fourth-degree exponential polynomial. Then we apply the obtained results to a simplified bidirectional associated memory (BAM) neural network with four neurons and multiple time delays. By taking the sum of the delays as the bifurcation parameter, it is shown that under certain assumptions the steady state is absolutely stable. Under another set of conditions, there are some critical values of the delay, when the delay crosses these critical values, the Hopf bifurcation occurs. Furthermore, some explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and center manifold reduction. Numerical simulations supporting the theoretical analysis are also included.

Suggested Citation

  • Xiang-Ping Yan & Wan-Tong Li, 2006. "Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-29, February.
    • Handle: RePEc:hin:jnddns:032529
    DOI: 10.1155/DDNS/2006/32529
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    Cited by:

    1. Sun, Dandan & Teng, Zhidong & Wang, Kai & Zhang, Tailei, 2023. "Stability and Hopf bifurcation in delayed age-structured SVIR epidemic model with vaccination and incubation," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. 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.

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