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Hopf Bifurcation Analysis for a Four‐Dimensional Recurrent Neural Network with Two Delays

Author

Listed:
  • Zizhen Zhang
  • Huizhong Yang

Abstract

A four‐dimensional recurrent neural network with two delays is considered. The main result is given in terms of local stability and Hopf bifurcation. Sufficient conditions for local stability of the zero equilibrium and existence of the Hopf bifurcation with respect to both delays are obtained by analyzing the distribution of the roots of the associated characteristic equation. In particular, explicit formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form theory and center manifold theory. Some numerical examples are also presented to verify the theoretical analysis.

Suggested Citation

  • Zizhen Zhang & Huizhong Yang, 2013. "Hopf Bifurcation Analysis for a Four‐Dimensional Recurrent Neural Network with Two Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:436254
    DOI: 10.1155/2013/436254
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    References listed on IDEAS

    as
    1. Changjin Xu & Xiaofei He, 2011. "Stability and Bifurcation Analysis in a Class of Two-Neuron Networks with Resonant Bilinear Terms," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-21, June.
    2. Changjin Xu & Xiaofei He, 2011. "Stability and Bifurcation Analysis in a Class of Two‐Neuron Networks with Resonant Bilinear Terms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    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.
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