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Stability and Hopf Bifurcation of a Three-Neuron Network with Multiple Discrete and Distributed Delays

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Abstract

In this paper, a class of three-neuron network with discrete and distributed delays is introduced. We first give a detailed Hopf bifurcation analysis for the proposed network. Choosing the discrete time delay as a bifurcation parameter, the existence of Hopf bifurcation is studied. Moreover, by using the normal form theory and center manifold theorem, the formulae determining the direction of the bifurcations and the stability of the bifurcating periodic solutions are derived. Finally, numerical simulations are presented to demonstrate the effectiveness of our theoretical results.

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Author information

Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Zhen Wang & Li Li

  2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    Zhen Wang & Yuxia Li

  3. College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, 266061, China

    Zunshui Cheng

Authors
  1. Zhen Wang
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  2. Li Li
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  3. Yuxia Li
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  4. Zunshui Cheng
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Corresponding author

Correspondence to Zhen Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 61573008, 61473178, 61473177, 61503002), Post-Doctoral Applied Research Projects of Qingdao (No. 2016115) and SDUST Research Fund (No. 2014TDJH102).

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Cite this article

Wang, Z., Li, L., Li, Y. et al. Stability and Hopf Bifurcation of a Three-Neuron Network with Multiple Discrete and Distributed Delays. Neural Process Lett 48, 1481–1502 (2018). https://doi.org/10.1007/s11063-017-9754-8

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  • DOI: https://doi.org/10.1007/s11063-017-9754-8

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