https://doi.org/10.1140/epjs/s11734-025-02039-3
Regular Article
Topological interactions and elastic coupling in a class of VO
-based memristive neural circuit models
1
Department of Physics, Lanzhou University of Technology, Qilihe District, 730050, Lanzhou, Gansu, China
2
School of Equipment Engineering, Shenyang Ligong University, 110159, Shenyang, Liaoning, China
3
Lanzhou Center for Theoretical Physics, Key Laboratory of Quantum Theory and Applications of MoE, and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, 730000, Lanzhou, Gansu, China
Received:
22
June
2025
Accepted:
20
October
2025
Published online:
30
October
2025
Kirchhoff-based circuit models capture pairwise electrical interactions, but cannot represent collective dynamics generated by higher-order, multiphysics couplings. In this paper, we investigate VO-based memristive neuronal networks extended by higher-order topological interactions and elastic coupling. By embedding neurons on deformable simplicial structures, we demonstrate how membrane deformation dynamically modulates capacitive connectivity and produces emergent collective behaviors. Numerical simulations reveal bifurcations from equilibria to oscillations in single neurons, synchronization and multistability in triangular motifs, and multifrequency as well as chaotic-like regimes in tetrahedral networks. These results highlight how elastic simplices enrich dynamics beyond Kirchhoff-type models, offering a physically grounded framework for topological neuromorphic circuit design.
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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.
