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Stability and Hopf Bifurcation of an n‐Neuron Cohen‐Grossberg Neural Network with Time Delays

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  • Qiming Liu
  • Sumin Yang

Abstract

A Cohen‐Grossberg neural network with discrete delays is investigated in this paper. Sufficient conditions for the existence of local Hopf bifurcation are obtained by analyzing the distribution of roots of characteristic equation. Moreover, the direction and stability of Hopf bifurcation are obtained by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the obtained results.

Suggested Citation

  • Qiming Liu & Sumin Yang, 2014. "Stability and Hopf Bifurcation of an n‐Neuron Cohen‐Grossberg Neural Network with Time Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:468584
    DOI: 10.1155/2014/468584
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    References listed on IDEAS

    as
    1. Qiming Liu & Wang Zheng, 2012. "Bifurcation of a Cohen-Grossberg Neural Network with Discrete Delays," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, April.
    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.
    3. Huang, Zhenkun & Xia, Yonghui, 2009. "Exponential periodic attractor of impulsive BAM networks with finite distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 373-384.
    4. Qiming Liu & Wang Zheng, 2012. "Bifurcation of a Cohen‐Grossberg Neural Network with Discrete Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    Full references (including those not matched with items on IDEAS)

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