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Stability and Hopf Bifurcation Analysis of an (n + m)-Neuron Double-Ring Neural Network Model with Multiple Time Delays

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Abstract

Up till the present moment, researchers have always featured the single-ring neural network. These investigations, however, disregard the link between rings in neural networks. This paper highlights a high-dimensional double-ring neural network model with multiple time delays. The neural network has two rings of a shared node, where one ring has n neurons and the other has m + 1 neurons. By utilizing the sum of time delays as the bifurcation parameter, the method of Coates’ flow graph is applied to obtain the relevant characteristic equation. The stability of the neural network model with bicyclic structure is discussed by dissecting the characteristic equation, and the critical value of Hopf bifurcation is derived. The effect of the sum of time delays and the number of neurons on the stability of the model is extrapolated. The validity of the theory can be verified by numerical simulations.

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Authors and Affiliations

  1. College of Automation and College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Ruitao Xing, Min Xiao & Yuezhong Zhang

  2. School of Automation and Electrical Engineering, Linyi University, Linyi, 276000, China

    Jianlong Qiu

Authors
  1. Ruitao Xing
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  2. Min Xiao
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  3. Yuezhong Zhang
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  4. Jianlong Qiu
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Corresponding author

Correspondence to Min Xiao.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 61573194, 62073172, 61877033, and the Natural Science Foundation of Jiangsu Province of China under Grant No. BK20181389.

This paper was recommended for publication by Editor XIN Bin.

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Xing, R., Xiao, M., Zhang, Y. et al. Stability and Hopf Bifurcation Analysis of an (n + m)-Neuron Double-Ring Neural Network Model with Multiple Time Delays. J Syst Sci Complex 35, 159–178 (2022). https://doi.org/10.1007/s11424-021-0108-2

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  • DOI: https://doi.org/10.1007/s11424-021-0108-2

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