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Bifurcation Analysis in a Three-Neuron Artificial Neural Network Model with Distributed Delays

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Abstract

In this paper, a three-neuron artificial neural network model with distributed delays is considered. Its dynamics is investigated in term of the linear stability analysis and Hopf bifurcation analysis. By regarding the sum of two delays as a bifurcation parameter and analyzing the associated characteristic equation, we find that Hopf bifurcation occurs when the bifurcation parameter passes through some certain values. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using the normal form method and center manifold theory. Finally, computer simulations are given to support the theoretical predictions.

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Acknowledgments

This work is supported by National Natural Science Foundation of China (No. 11261010, No. 11201138 and No. 11101126), Natural Science and Technology Foundation of Guizhou Province (J[2015]2025) and Scientific Research Fund of Hunan Provincial Education Department (No. 12B034).

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Authors and Affiliations

  1. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, 550004, People’s Republic of China

    Changjin Xu

  2. College of Science, Hunan University of Technology, Zhuzhou, 412007, People’s Republic of China

    Qiming Zhang

  3. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, People’s Republic of China

    Yusen Wu

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  1. Changjin Xu
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  2. Qiming Zhang
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  3. Yusen Wu
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Correspondence to Changjin Xu.

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Xu, C., Zhang, Q. & Wu, Y. Bifurcation Analysis in a Three-Neuron Artificial Neural Network Model with Distributed Delays. Neural Process Lett 44, 343–373 (2016). https://doi.org/10.1007/s11063-015-9461-2

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  • DOI: https://doi.org/10.1007/s11063-015-9461-2

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