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Bifurcation delay in a network of nonlocally coupled slow-fast FitzHugh–Nagumo neurons

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

Many slow-fast systems can exhibit delayed bifurcation, which means that the crucial transition occurs after some delay during the transition between the oscillatory and steady states due to the presence of a slowly varying parameter. We specifically analyze the dynamical behavior of bifurcation delay in a network of nonlocally coupled FitzHugh–Nagumo neurons by adjusting the frequency of slowly varying currents. Interestingly, we observe an appearance of chimera-like states despite a tiny parameter mismatch in the frequency of any single node. The observed chimera-like state is evidenced through the mean-phase velocity profile. The robustness of the obtained results is then tested by perturbing multiple neurons in three different ways: constant, linearly increasing, and decreasing frequency of certain nodes. Importantly, we discover that the observed chimera state is resilient to all perturbations.

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Data availability statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

M. Rhaima was supported by the Researchers Supporting Project number (RSPD2024R683) King Saud University, Riyadh, Saudi Arabia. SS and PD acknowledges with gratitude that this work was funded by the Centre for Nonlinear Systems, Chennai Institute of Technology (CIT), India, under funding number CIT/CNS/2024/RP-005. PD is partially supported by National Natural Science Foundation of china (NSFC) No. 12375031 and Scientific research start-up project (2024) No. 24BS104.

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Authors and Affiliations

  1. Institute of Systems Science, Huaqiao University, Xiamen, 361021, China

    Premraj Durairaj

  2. College of Information Science and Engineering, Huaqiao University, Xiamen, 361021, China

    Premraj Durairaj

  3. College of Mechanical Engineering and Automation, Huaqiao University, Xiamen, 361021, China

    Premraj Durairaj

  4. Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamil Nadu, 600 069, India

    Premraj Durairaj & Saravanan Shanmugam

  5. Department of Mechanical Engineering, Chennai Institute of Technology, Chennai, Tamil Nadu, 600 069, India

    Prasanth Durairaj

  6. Department of Statistics and Operations Research, College of Sciences, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    Mohamed Rhaima

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  1. Premraj Durairaj
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  2. Saravanan Shanmugam
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  3. Prasanth Durairaj
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  4. Mohamed Rhaima
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All the authors contributed equally to the preparation of this manuscript.

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Correspondence to Premraj Durairaj.

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Durairaj, P., Shanmugam, S., Durairaj, P. et al. Bifurcation delay in a network of nonlocally coupled slow-fast FitzHugh–Nagumo neurons. Eur. Phys. J. B 97, 62 (2024). https://doi.org/10.1140/epjb/s10051-024-00707-2

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  • DOI: https://doi.org/10.1140/epjb/s10051-024-00707-2