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Dynamical Behavior Analysis of a Neutral-Type Single Neuron System

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Advances in Neural Networks – ISNN 2018 (ISNN 2018)

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Abstract

In this paper, the equation used to describe a single neuron system of neutral-type with one delay is studied. By using a suitable Lyapunov function, we derive sufficient conditions of globally asymptotic stability of the zero equilibrium point of this equation. Moreover, the criterions of the existence of Hopf bifurcation that gives rise to self-sustained oscillation are obtained. Finally, the perturbation theory is used to acquire the expansion of oscillation to any order on the basis of the coefficient of the fundamental frequency, and the frequency-amplitude relations about the second order are carefully discussed.

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Acknowledgments

This work is supported by National Key Research and Development Program of China (Grant no. 2016YFB0800601), Natural Science Foundation of China (Grant no. 61472331, 61772434).

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Authors and Affiliations

  1. The Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Southwest University, Chongqing, 400715, People’s Republic of China

    Qiuyu Lv, Nankun Mu & Xiaofeng Liao

Authors
  1. Qiuyu Lv
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  2. Nankun Mu
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  3. Xiaofeng Liao
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Corresponding authors

Correspondence to Nankun Mu or Xiaofeng Liao .

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Editors and Affiliations

  1. Texas A&M University at Qatar, Doha, Qatar

    Tingwen Huang

  2. Sichuan University, Chengdu, China

    Jiancheng Lv

  3. Southeast University, Nanjing, China

    Changyin Sun

  4. United Institute of Informatics Problems, Minsk, Belarus

    Alexander V. Tuzikov

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Lv, Q., Mu, N., Liao, X. (2018). Dynamical Behavior Analysis of a Neutral-Type Single Neuron System. In: Huang, T., Lv, J., Sun, C., Tuzikov, A. (eds) Advances in Neural Networks – ISNN 2018. ISNN 2018. Lecture Notes in Computer Science(), vol 10878. Springer, Cham. https://doi.org/10.1007/978-3-319-92537-0_38

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  • DOI: https://doi.org/10.1007/978-3-319-92537-0_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-92536-3

  • Online ISBN: 978-3-319-92537-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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