https://doi.org/10.1140/epjs/s11734-026-02384-x
Regular Article
Extreme-event dynamics under linear and nonlinear higher-order coupling in FitzHugh–Nagumo networks
1
Department of Mathematics, M.Kumarasamy College of Engineering, 639113, Karur, India
2
Centre for Artificial Intelligence, Easwari Engineering College, 600089, Chennai, Tamil Nadu, India
3
Center for Cognitive Science, Trichy SRM Medical College Hospital and Research Center, Trichy, Tamil Nadu, India
4
Department of Mathematics, Periyar University, 636011, Salem, Tamil Nadu, India
a
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Received:
5
April
2026
Accepted:
9
May
2026
Published online:
19
May
2026
Abstract
Rare large-amplitude excursions, conventionally termed extreme events, can disproportionately influence the long-term collective dynamics of coupled excitable networks despite their low frequency of occurrence. Higher-order interactions, which couple three or more units simultaneously, are known to reshape collective dynamics in complex networks, but their influence on extreme-event activity has received little systematic attention. We address this question in a heterogeneous, globally coupled FitzHugh–Nagumo network by comparing two structurally distinct higher-order coupling schemes: a linear additive correction to the standard pairwise diffusive coupling, and an explicit nonlinear three-body interaction. The underlying pairwise network already produces rare large mean-field excursions, so the central question is how each higher-order scheme modifies this existing behaviour. Under a common numerical and extreme-value analysis framework, we find that the linear scheme preserves a broader region of extreme-event activity in parameter space, while the nonlinear three-body scheme contracts it considerably. An analytical mean-field reduction explains the mechanism: the linear coupling is algebraically equivalent to a rescaled pairwise diffusion and introduces no new mean-field dynamics, whereas the nonlinear coupling generates a negative feedback proportional to the spatial spread of node voltages, suppressing large collective excursions precisely when the network is most predisposed to produce them. These findings demonstrate that the algebraic form of higher-order interactions, not their amplitude, determines whether such couplings broaden or suppress extreme-event activity in excitable networks.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
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.
