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Hopf-Pitchfork Bifurcation Analysis of a Coupled Neural Oscillator System with Excitatory-to-Inhibitory Connection and Time Delay

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Advances in Neural Networks – ISNN 2018 (ISNN 2018)

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Abstract

In this paper, a coupled neural oscillator system with excitatory-to-inhibitory connection and time delay is considered. First, the existence of pitchfork bifurcation and the equilibrium patterns are investigated. It is found that the system has one, three and five equilibria with self-connection weight increasing. Then, by choosing the self-connection weight and communication delay as the two bifurcation parameters, the conditions where Hopf-pitchfork bifurcation occurs are obtained. Analyzing the bifurcation diagram, we find that the system exhibits many complex phenomena such as co-existence of two synchronous equilibria or two anti-synchronous equilibria, two stable periodic solutions, and two quasi-periodic attractors, which are validated by numerical simulations.

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Acknowledgments

This paper is partially funded by National Priority Research Project NPRP 9 166-1-031, funded by Qatar National Research Fund.

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Authors and Affiliations

  1. School of Electronics and Information Engineering, Southwest University, Chongqing, 400715, China

    Lei Yang & Tao Dong

  2. Texas A&M University, Doha, 23874, Qatar

    Tingwen Huang

Authors
  1. Lei Yang
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  2. Tao Dong
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  3. Tingwen Huang
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Corresponding author

Correspondence to Lei Yang .

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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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Yang, L., Dong, T., Huang, T. (2018). Hopf-Pitchfork Bifurcation Analysis of a Coupled Neural Oscillator System with Excitatory-to-Inhibitory Connection and Time Delay. 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_46

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  • DOI: https://doi.org/10.1007/978-3-319-92537-0_46

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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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