https://doi.org/10.1140/epjs/s11734-025-01612-0
Regular Article
Impact of nonlinear boundary conditions on spiral wave formation in reaction–diffusion FitzHugh–Nagumo system
Department of Basic Course, Shaanxi Railway Institute, 714000, Weinan, Shaanxi, China
Received:
7
February
2025
Accepted:
29
March
2025
Published online:
19
April
2025
Nonlinear boundary conditions are essential for modeling more realistic systems in various fields, including biology, chemistry, and physics. In the context of biological systems, this boundary condition can model a neuronal membrane or other excitable media, where ion flow at the boundary is influenced by both the membrane potential and the recovery variable. This paper proposes nonlinear boundary conditions for the reaction–diffusion FitzHugh–Nagumo system. Pattern formation, especially spiral waves, is explored under nonlinear Dirichlet and Neumann boundary conditions. The results represent that the patterns are more regular in the homogeneous Neumann boundary condition than the nonlinear ones. While the nonlinear boundary conditions introduce significant boundary-driven effects, leading to fragmented, asymmetrical, and distorted patterns.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.