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Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model

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  • Lu, Lulu
  • Ge, Mengyan
  • Xu, Ying
  • Jia, Ya

Abstract

Noise and time delay are ubiquitous in various physical and biological systems. In this paper, we studied the phase synchronization and mode transition of oscillation mode induced by time delays and noises in a coupled FitzHugh–Nagumo (FHN) neural system. In the case of coupled neurons with single time delay, it is found that the mode oscillation of neurons induced by the noise and time delay undergoes a successive transitions from the synchronization, the out-of phase, the alternating phase-drift and anti-phase state, to the anti-phase state. In the case of coupled neurons with two time delays, when the two delays are comparable, the large amplitude oscillation of potential is in alternating synchronous and asynchronous state in the absence of noises, and the small amplitude oscillation of potential is always synchronized. The oscillation behaviors of coupled neurons with two time delays are similar to the cases with a single time delay in the presence of noises. When one of two time delays is largely dominant over the other, the neurons show completely different dynamic behaviors.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:535:y:2019:i:c:s0378437119313937
    DOI: 10.1016/j.physa.2019.122419
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    Cited by:

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    2. Gui, Rong & Li, Jiaxin & Yao, Yuangen & Cheng, Guanghui, 2021. "Effect of time-delayed feedback in a bistable system inferred by logic operation," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Cesar Manchein & Paulo C. Rech, 2024. "Effects of external stimuli on the dynamics of deterministic and stochastic Hindmarsh–Rose neuron models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(8), pages 1-16, August.
    4. Zhang, Gang & Shu, Yichen & Zhang, Tianqi, 2022. "The study on dynamical behavior of FitzHugh–Nagumo neural model under the co-excitation of non-Gaussian and colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    5. Lin, Yi & Liu, Wenbo & Hang, Cheng, 2023. "Revelation and experimental verification of quasi-periodic bursting, periodic bursting, periodic oscillation in third-order non-autonomous memristive FitzHugh-Nagumo neuron circuit," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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