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Stability and Hopf bifurcation analysis of a complex-valued Wilson–Cowan neural network with time delay

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  • JI, Conghuan
  • QIAO, Yuanhua
  • MIAO, Jun
  • DUAN, Lijuan

Abstract

Stability and Hopf bifurcation of a class of delayed complex-valued neural networks are investigated in this paper. First, using proper translations and coordinate transformations, we decompose the activation functions and connection weights into their real and imaginary parts, so as to construct an equivalent real-valued system. Then, the sufficient conditions for Hopf bifurcation and its directions are provided through normal form theory and central manifold theorem. In the end, some numerical simulations are given to illustrate the correctness of the results.

Suggested Citation

  • JI, Conghuan & QIAO, Yuanhua & MIAO, Jun & DUAN, Lijuan, 2018. "Stability and Hopf bifurcation analysis of a complex-valued Wilson–Cowan neural network with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 45-61.
    • Handle: RePEc:eee:chsofr:v:115:y:2018:i:c:p:45-61
    DOI: 10.1016/j.chaos.2018.04.022
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    References listed on IDEAS

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    1. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
    2. Dong, Tao & Hu, Wenjie & Liao, Xiaofeng, 2016. "Dynamics of the congestion control model in underwater wireless sensor networks with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 130-136.
    3. Liao, Xiaofeng & Ran, Jiouhong, 2007. "Hopf bifurcation in love dynamical models with nonlinear couples and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 853-865.
    4. Song Guo & Bo Du, 2016. "Global Exponential Stability of Periodic Solution for Neutral-Type Complex-Valued Neural Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-10, September.
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    Cited by:

    1. Chen, Jing & Xiao, Min & Wu, Xiaoqun & Wang, Zhengxin & Cao, Jinde, 2022. "Spatiotemporal dynamics on a class of (n+1)-dimensional reaction–diffusion neural networks with discrete delays and a conical structure," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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