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Bogdanov–Takens singularity in the Hindmarsh–Rose neuron with time delay

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  • Li, Yingying
  • Wei, Zhouchao
  • Zhang, Wei
  • Perc, Matjaž
  • Repnik, Robert

Abstract

In this paper, we study the Bogdanov–Takens singularity in the Hindmarsh–Rose neuron model with time delay. We use the center manifold reduction and the normal form method, by means of which the dynamics near this nonhyperbolic equilibrium can be reduced to the study of the dynamics of the corresponding normal form restricted to the associated two-dimensional center manifold. We show that changes in the time delay length can lead to the saddle-node bifurcation, to the Hopf bifurcation, and to the homoclinic bifurcation.

Suggested Citation

  • Li, Yingying & Wei, Zhouchao & Zhang, Wei & Perc, Matjaž & Repnik, Robert, 2019. "Bogdanov–Takens singularity in the Hindmarsh–Rose neuron with time delay," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 180-188.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:180-188
    DOI: 10.1016/j.amc.2019.02.046
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    References listed on IDEAS

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    1. Bandyopadhyay, Abhirup & Kar, Samarjit, 2018. "Impact of network structure on synchronization of Hindmarsh–Rose neurons coupled in structured network," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 194-212.
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    Cited by:

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    2. Lu, Lulu & Ge, Mengyan & Xu, Ying & Jia, Ya, 2019. "Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).

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