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Delay-induced bifurcation in a tri-neuron fractional neural network

Author

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  • Chengdai Huang
  • Jinde Cao
  • Zhongjun Ma

Abstract

This paper investigates the issue of stability and bifurcation for a delayed fractional neural network with three neurons by applying the sum of time delays as the bifurcation parameter. Based on fractional Laplace transform and the method of stability switches, some explicit conditions for describing the stability interval and emergence of Hopf bifurcation are derived. The analysis indicates that time delay can effectively enhance the stability of fractional neural networks. In addition, it is found that the stability interval can be varied by regulating the fractional order if all the parameters are fixed including time delay. Finally, numerical examples are presented to validate the derived theoretical results.

Suggested Citation

  • Chengdai Huang & Jinde Cao & Zhongjun Ma, 2016. "Delay-induced bifurcation in a tri-neuron fractional neural network," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(15), pages 3668-3677, November.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:15:p:3668-3677
    DOI: 10.1080/00207721.2015.1110641
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    Cited by:

    1. Wang, Yangling & Cao, Jinde & Huang, Chengdai, 2024. "Bifurcations of a fractional three-layer neural network with different delays: Delay-dependent and order-dependent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    2. Huang, Chengdai & Meng, Yijie & Cao, Jinde & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "New bifurcation results for fractional BAM neural network with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 31-44.
    3. 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.

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