https://doi.org/10.1140/epjs/s11734-024-01193-4
Regular Article
Dynamics of delayed and diffusive FitzHugh–Nagumo network
1
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, 450046, Zhengzhou, China
2
Institute of Applied Physics and Computational Mathematics, 100094, Beijing, China
b phdshen@126.com, xcjwshen@gmail.com
c
hu_xiaoyan@iapcm.ac.cn
Received:
9
January
2024
Accepted:
4
June
2024
Published online:
18
June
2024
Higher-order networks reveal intricate structural connections within neural brain models by exposing relationships between multiple nodes. Within human brain networks, information transmission among neurons invariably incurs a time delay, resulting in abnormal discharge of membrane potential. In this study, we analyze correlation visualizations of the Laplacian matrix derived from both general networks and higher-order networks, highlighting eigenvector distributions. The presence of time delay significantly influences the dynamical behavior of the system. Therefore, we examine the phase diagram, identifying firing patterns such as fast-spiking and mixed-mode oscillations. Ultimately, we demonstrate that both time delay and diffusion can alter the dynamical behavior of the FitzHugh–Nagumo model. Notably, within higher-order networks, the phenomenon of Turing instability becomes more pronounced, offering an analogous framework for studying associated diseases. This instability emerges as neuronal states approach abnormal levels, leading to the onset of related diseases. Numerical simulation and data also verify these results.
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© The Author(s), under exclusive licence to EDP Sciences, 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.
