https://doi.org/10.1140/epjb/s10051-024-00707-2
Regular Article - Statistical and Nonlinear Physics
Bifurcation delay in a network of nonlocally coupled slow-fast FitzHugh–Nagumo neurons
1
Institute of Systems Science, Huaqiao University, 361021, Xiamen, China
2
College of Information Science and Engineering, Huaqiao University, 361021, Xiamen, China
3
College of Mechanical Engineering and Automation, Huaqiao University, 361021, Xiamen, China
4
Center for Nonlinear Systems, Chennai Institute of Technology, 600 069, Chennai, Tamil Nadu, India
5
Department of Mechanical Engineering, Chennai Institute of Technology, 600 069, Chennai, Tamil Nadu, India
6
Department of Statistics and Operations Research, College of Sciences, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia
Received:
9
January
2024
Accepted:
30
April
2024
Published online:
17
May
2024
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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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
